Calculators / Linear Algebra / Matrix Addition Calculator

Matrix Addition Calculator

Published on: September 7 2025

This Matrix Addition Calculator helps you add two matrices and shows each step clearly. It works by adding the corresponding entries from matrices of the same dimensions to form a new matrix. This makes it useful for checking answers, understanding how matrix addition works, and practising linear algebra step by step.

Step-by-step method

  1. Make sure both matrices have the same dimensions.
  2. Add corresponding entries (same position) together.

Formula:

If A = [aij] and B = [bij], then A + B = [aij + bij].

Example 1: 2×2 matrices

Step 1 - Make sure both matrices have the same dimensions.

In this problem: Both matrices are 2×2, so they can be added.

12
-3
40
7
+
5
18
-9
2

Step 2 - Add corresponding entries (same position) together.

In this problem: Add entries in the same position to form the result matrix.

12+5
-3+18
40+-9
7+2
=
17
15
31
9

Final answer:

17
15
31
9

Example 2: 3×3 matrices

Step 1 - Make sure both matrices have the same dimensions.

In this problem: Both matrices are 3×3, so they can be added.

1000
-2
33
4
15
6
7
8
9
+
1
2
30
4
5
6
-7
0
11

Step 2 - Add corresponding entries (same position) together.

In this problem: Add entries in the same position to form the result matrix.

1000+1
-2+2
33+30
4+4
15+5
6+6
7+-7
8+0
9+11
=
1001
0
63
8
20
12
0
8
20

Final answer:

1001
0
63
8
20
12
0
8
20
Matrix A
+
Matrix B