Matrix Addition Calculator

Add two matrices element-wise with dimension validation and step-by-step output.

About Matrix Addition Calculator

Matrix addition adds corresponding elements of two matrices of the same dimensions. If A and B are both m×n matrices, then (A+B)ᵢⱼ = Aᵢⱼ + Bᵢⱼ.

Formula

Matrix Addition

(A + B)ᵢⱼ = Aᵢⱼ + Bᵢⱼ

A: First matrix
B: Second matrix

Worked example

With the default values below, Matrix Addition Calculator returns A + B of 6 8 10 12. Change any input above and every figure here is recalculated in your browser.

Inputs used

Matrix A (rows separated by newlines or semicolons; values by commas or spaces): 1 2 3 4
Matrix B: 5 6 7 8

Results

A + B: 6 8 10 12
Dimensions: 2×2

Step by step

1Matrix A= 1 2 3 4
2Matrix B= 5 6 7 8
3A + B (element-wise)= 6 8 10 12

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Can I add matrices of different sizes?

No. Matrix addition requires both matrices to have the same dimensions (same number of rows and columns).

Is matrix addition commutative?

Yes. A + B = B + A for all conforming matrices, since addition of real numbers is commutative.