Matrix Addition Calculator

About Matrix Addition Calculator

Matrix addition is the simplest of the matrix operations: add the entries in matching positions. The entry in row 2, column 3 of the result is just the sum of the entries in row 2, column 3 of each input. The only rule is that both matrices must have exactly the same dimensions, since there is nothing to add a value to if the other matrix has no entry in that position. A 2x3 can only be added to another 2x3. This calculator checks the dimensions first and tells you what the mismatch is rather than producing a partial result. Unlike multiplication, addition is commutative and associative, so A + B equals B + A and the grouping of three or more matrices does not matter. Subtraction works identically but with the signs reversed, and is available as a separate tab. Set the size of both grids, type the values, and the result updates as you go. For multiplication, which follows a very different rule, see Matrix Multiplication Calculator.

How to use Matrix Addition Calculator

  1. Select an operation from the tab bar (Add, Multiply, etc.)
  2. Set matrix dimensions and enter values in the grid cells
  3. See the result matrix or scalar instantly

Frequently Asked Questions

How do you add two matrices?
Add the entries in matching positions. The value in row i, column j of the result is the sum of the values in row i, column j of each input matrix. Nothing else is involved.
Can you add matrices of different sizes?
No. Both matrices must have exactly the same number of rows and the same number of columns. There is no meaningful way to add a 2x3 to a 3x2, and the operation is simply undefined.
Is matrix addition commutative?
Yes. A + B always equals B + A, and addition is associative too, so the grouping of three or more matrices does not change the result. This is unlike multiplication, where order matters.
What is the zero matrix?
A matrix of all zeros. Adding it leaves the other matrix unchanged, so it plays the same role that 0 plays in ordinary addition.
How is subtraction different?
It is the same element by element operation with the signs reversed, and it has the same dimension requirement. Note that A minus B is not the same as B minus A.

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