Add two matrices
Both matrices must have the same number of rows and columns. Supports matrices from 1 × 1 to 8 × 8.
How matrix addition works
Matrix addition is an element-wise operation. If two matrices have the same dimensions, add the numbers occupying corresponding positions. The resulting matrix has the same dimensions as the original matrices.
1. Check the dimensions
Both matrices must have the same shape. A 2 × 3 matrix can be added to another 2 × 3 matrix, but not to a 3 × 2 matrix.
2. Add matching entries
Add the entry in row i and column j of A to the entry in row i and column j of B.
3. Form the result
Place each sum in the same position in C. The result retains the dimensions of A and B.
Worked example
The result is a 2 × 2 matrix: [[6, 8], [10, 12]].
Properties of matrix addition
Commutative property
Changing the order does not change the sum: A + B = B + A.
Associative property
For matrices with matching dimensions, (A + B) + C = A + (B + C).
Zero matrix
Adding a zero matrix of the same dimensions leaves a matrix unchanged: A + 0 = A.
Additive inverse
Adding the negative of a matrix produces the zero matrix: A + (−A) = 0.
Frequently asked questions
How do you add two matrices?
Make sure both matrices have the same number of rows and columns. Add each entry in the first matrix to the entry in the corresponding position in the second matrix.
Can matrices with different dimensions be added?
No. Standard matrix addition requires the same number of rows and the same number of columns in both matrices.
Does the result have the same dimensions?
Yes. Adding two m × n matrices produces another m × n matrix.
Can I add matrices containing decimals or negative numbers?
Yes. Enter integers, decimal numbers or negative values in the matrix cells. The calculator validates entries before calculating.
What is the difference between matrix addition and multiplication?
Addition combines corresponding entries and requires matching dimensions. Matrix multiplication uses row-by-column products and requires the first matrix's column count to equal the second matrix's row count.
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