Calculators / Algebra 2 / 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. In Algebra 2, matrix addition is one of the basic matrix operations used when working with systems, transformations, and organized numerical data. It works by adding corresponding entries from matrices of the same dimensions to form a new matrix.

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