Addition & Subtraction of Matrices

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 = [aij]m×n

B = [bij]m×n

A + B = [aij + bij]m×n

A − B = A + (−B) = [aij]m×n + [−bij]m×n

= [aij − bij]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