Two matrices A and B can be added provided both the matrices are of the same order and their sum A + B is obtained by adding the corresponding entries of both the matrices A and B.

A = [a_{ij}]_{m×n}

B = [b_{ij}]m×n

A + B = [a_{ij} + b_{ij}]_{m×n}

A − B = A + (−B) = [a_{ij}]_{m×n} + [−b_{ij}]_{m×n}

= [a_{ij} − b_{ij}]_{m×n}

The matrices A + B and A −B have same order equal to the order of A or B.

Subtraction is treated as negative addition.

The additive inverse of matrix A is −A.

A + (−A) = (−A) + A = O = zero matrix