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