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Complete guide to 2D arrays in C including declaration, initialization, matrix operations, row-column access patterns, and practical examples with memory diagrams.
A two-dimensional array is essentially an array of arrays — it organizes data in a tabular format with rows and columns. If you think of a 1D array as a single row of boxes, a 2D array is a grid or matrix of boxes arranged in rows and columns.
2D arrays are everywhere in programming: storing matrices for mathematical operations, representing game boards, managing tabular data like spreadsheets, and handling image pixel data.
Declaration of 2D Arrays
The general syntax for declaring a two-dimensional array is:
Example
data_type array_name[rows][columns];
Examples:
Example
int matrix[3][4]; // 3 rows, 4 columns — 12 integers
float table[5][5]; // 5×5 table of floats
char grid[10][10]; // 10×10 character grid
Memory Layout: Row-Major Order
Although we think of 2D arrays as grids, memory is linear. C stores 2D arrays in row-major order — all elements of row 0 come first, then row 1, and so on.
int matrix[3][4] = {
{1, 2, 3, 4}, // Row 0
{5, 6, 7, 8}, // Row 1
{9, 10, 11, 12} // Row 2
};
Logical View (Grid):
Col 0 Col 1 Col 2 Col 3
Row 0 [ 1 | 2 | 3 | 4 ]
Row 1 [ 5 | 6 | 7 | 8 ]
Row 2 [ 9 | 10 | 11 | 12 ]
Physical Memory (Linear - Row Major):
┌───┬───┬───┬───┬───┬───┬───┬───┬───┬────┬────┬────┐
│ 1 │ 2 │ 3 │ 4 │ 5 │ 6 │ 7 │ 8 │ 9 │ 10 │ 11 │ 12 │
└───┴───┴───┴───┴───┴───┴───┴───┴───┴────┴────┴────┘
[0][0] [0][1] [0][2] [0][3] [1][0] [1][1] ...
Address of matrix[i][j] = Base + (i × columns + j) × sizeof(int)
Initialization Methods
Method 1: Nested Braces (Recommended)
Example
int matrix[3][3] = {
{1, 2, 3},
{4, 5, 6},
{7, 8, 9}
};
Method 2: Flat Initialization
Example
int matrix[3][3] = {1, 2, 3, 4, 5, 6, 7, 8, 9};
// Fills row by row: {1,2,3}, {4,5,6}, {7,8,9}
Method 3: Partial Initialization
Example
int matrix[3][3] = {
{1, 2}, // Row 0: {1, 2, 0}
{4}, // Row 1: {4, 0, 0}
{7, 8, 9} // Row 2: {7, 8, 9}
};
Method 4: Omitting Row Size
You can omit the first dimension (rows) when initializing, but the second dimension (columns) is always required:
Example
int matrix[][3] = {
{1, 2, 3},
{4, 5, 6}
};
// Compiler infers 2 rows
Accessing and Modifying Elements
Example
#include <stdio.h>
int main() {
int matrix[3][3] = {
{1, 2, 3},
{4, 5, 6},
{7, 8, 9}
};
// Access specific element
printf("Element at [1][2] = %d\n", matrix[1][2]); // 6
// Modify element
matrix[0][0] = 100;
printf("Modified [0][0] = %d\n", matrix[0][0]); // 100
return 0;
}
Output
Element at [1][2] = 6 Modified [0][0] = 100
Reading and Displaying a 2D Array
Example
#include <stdio.h>
int main() {
int rows = 3, cols = 3;
int matrix[3][3];
// Input
printf("Enter elements of 3x3 matrix:\n");
for (int i = 0; i < rows; i++) {
for (int j = 0; j < cols; j++) {
printf(" [%d][%d]: ", i, j);
scanf("%d", &matrix[i][j]);
}
}
// Display
printf("\nMatrix:\n");
for (int i = 0; i < rows; i++) {
for (int j = 0; j < cols; j++) {
printf("%4d", matrix[i][j]);
}
printf("\n");
}
return 0;
}
Output
Enter elements of 3x3 matrix: [0][0]: 1 [0][1]: 2 [0][2]: 3 [1][0]: 4 [1][1]: 5 [1][2]: 6 [2][0]: 7 [2][1]: 8 [2][2]: 9 Matrix: 1 2 3 4 5 6 7 8 9
Matrix Operations
Matrix Addition
Example
#include <stdio.h>
int main() {
int a[2][3] = {{1, 2, 3}, {4, 5, 6}};
int b[2][3] = {{7, 8, 9}, {10, 11, 12}};
int result[2][3];
// Addition
for (int i = 0; i < 2; i++) {
for (int j = 0; j < 3; j++) {
result[i][j] = a[i][j] + b[i][j];
}
}
// Display result
printf("Sum of matrices:\n");
for (int i = 0; i < 2; i++) {
for (int j = 0; j < 3; j++) {
printf("%4d", result[i][j]);
}
printf("\n");
}
return 0;
}
Output
Sum of matrices: 8 10 12 14 16 18
Matrix Multiplication
Example
#include <stdio.h>
int main() {
int a[2][3] = {{1, 2, 3}, {4, 5, 6}};
int b[3][2] = {{7, 8}, {9, 10}, {11, 12}};
int result[2][2] = {0};
// Multiply: (2×3) × (3×2) = (2×2)
for (int i = 0; i < 2; i++) {
for (int j = 0; j < 2; j++) {
for (int k = 0; k < 3; k++) {
result[i][j] += a[i][k] * b[k][j];
}
}
}
printf("Product:\n");
for (int i = 0; i < 2; i++) {
for (int j = 0; j < 2; j++) {
printf("%5d", result[i][j]);
}
printf("\n");
}
return 0;
}
Output
Product: 58 64 139 154
Matrix Transpose
Example
#include <stdio.h>
int main() {
int matrix[3][3] = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}};
int transpose[3][3];
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 3; j++) {
transpose[j][i] = matrix[i][j];
}
}
printf("Original:\n");
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 3; j++)
printf("%3d", matrix[i][j]);
printf("\n");
}
printf("\nTranspose:\n");
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 3; j++)
printf("%3d", transpose[i][j]);
printf("\n");
}
return 0;
}
Output
Original: 1 2 3 4 5 6 7 8 9 Transpose: 1 4 7 2 5 8 3 6 9
Row-wise and Column-wise Operations
Example
#include <stdio.h>
int main() {
int matrix[3][4] = {
{1, 2, 3, 4},
{5, 6, 7, 8},
{9, 10, 11, 12}
};
// Row-wise sum
printf("Row sums: ");
for (int i = 0; i < 3; i++) {
int sum = 0;
for (int j = 0; j < 4; j++)
sum += matrix[i][j];
printf("%d ", sum);
}
// Column-wise sum
printf("\nCol sums: ");
for (int j = 0; j < 4; j++) {
int sum = 0;
for (int i = 0; i < 3; i++)
sum += matrix[i][j];
printf("%d ", sum);
}
printf("\n");
return 0;
}
Output
Row sums: 10 26 42 Col sums: 15 18 21 24
Diagonal Elements
For square matrices, accessing diagonal elements is a common operation:
Example
#include <stdio.h>
int main() {
int matrix[3][3] = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}};
int n = 3;
printf("Primary diagonal: ");
for (int i = 0; i < n; i++)
printf("%d ", matrix[i][i]);
printf("\nSecondary diagonal: ");
for (int i = 0; i < n; i++)
printf("%d ", matrix[i][n - 1 - i]);
printf("\n");
return 0;
}
Output
Primary diagonal: 1 5 9 Secondary diagonal: 3 5 7
Interview Questions
Q1: Why must the column size be specified when declaring a 2D array in C?
The compiler needs the column count to calculate memory addresses. The address formula base + (i × cols + j) × sizeof(type) requires knowing cols. Without it, the compiler cannot determine where each row begins.
Q2: What's the difference between row-major and column-major order?
In row-major order (used by C), elements of each row are stored contiguously. In column-major order (used by Fortran), elements of each column are stored contiguously. This affects cache performance when traversing matrices.
Q3: How do you pass a 2D array to a function in C?
You must specify at least the column size: void func(int arr[][4], int rows). Alternatively, use a pointer: void func(int (*arr)[4], int rows). The row count is typically passed as a separate parameter.
Q4: Can you have a 2D array with different row lengths (jagged array) in C?
Not with static 2D arrays. However, you can simulate jagged arrays using an array of pointers, where each pointer points to a dynamically allocated row of different length.
Summary
- 2D arrays store data in a matrix format with rows and columns
- C uses row-major order for memory storage
- Column size must always be specified in declarations
- Address formula:
base + (i × cols + j) × sizeof(type) - Common operations: addition, multiplication, transpose, diagonal access
- Nested loops are the standard pattern for traversing 2D arrays
Continue the lesson path
Study next in this module
01ArraysPassing Arrays to Functions in CUnderstand how arrays are passed to functions in C, array decay to pointers, why size information is lost, and best practices for writing array-handling functions.02ArraysOne Dimensional Arrays in C ProgrammingMaster one-dimensional arrays in C with detailed examples covering declaration, initialization, traversal, input/output operations, and common array algorithms.03ArraysMultidimensional Arrays in C ProgrammingLearn about multidimensional arrays (3D and beyond) in C programming with practical examples, memory layout explanations, and real-world use cases.04ArraysIntroduction to Arrays in C ProgrammingLearn what arrays are in C, why we need them, how to declare and initialize arrays, and understand memory layout with practical examples.