Matrix Addition and Subtraction Calculator

A matrix is a rectangular array of numbers arranged in rows and columns. The size of a matrix is described by its dimensions — for example, a 3×2 matrix has 3 rows and 2 columns. Matrices are widely used in mathematics, physics, computer graphics, and data science.

To add two matrices, they must have the same number of rows and columns. You simply add the corresponding elements together — the element in row i, column j of Matrix A is added to the element in row i, column j of Matrix B. The result is a new matrix of the same dimensions.

Matrix subtraction works exactly like addition, but you subtract corresponding elements instead. Subtract the element at position [i][j] in Matrix B from the element at position [i][j] in Matrix A. The matrices must have identical dimensions for the operation to be valid.

No. Matrix addition and subtraction are only defined for matrices that have exactly the same number of rows and the same number of columns. If the dimensions don't match, the operation is undefined. This calculator requires you to set matching row and column counts for both matrices.

Yes, matrix addition is commutative, meaning A + B = B + A. It is also associative: (A + B) + C = A + (B + C). However, subtraction is not commutative — A − B is generally not equal to B − A.

Matrix addition combines two matrices of the same size by summing corresponding elements, producing a result of the same dimensions. Matrix multiplication is a more complex operation where the number of columns in the first matrix must equal the number of rows in the second, and the result can have different dimensions than either input.

Matrices are used extensively in computer graphics (transformations, rotations), physics (quantum mechanics, relativity), machine learning (representing datasets and weights), economics (input-output models), and engineering (solving systems of linear equations). Matrix addition specifically arises when combining data sets or superimposing transformations.

Yes. You can enter any positive or negative real number into any cell of Matrix A or Matrix B. The calculator will correctly add or subtract them element by element, including cases where the result is negative or zero.