4. Algebra of Matrices :
Addition : A + B = [aij + bij] where A & B are of the same type. (same order)
(a) Addition of matrices is commutative.
i.e. A + B = B + A where A and B must have the same order
(b) Addition of Matrix is associative. (A + B) + C = A + (B + C)
Provided A, B & C have the same order.
(c) Additive inverse . If A + B = O = B + A A = m x n
i.e . they have the same order then A and B are said to be the additive inverse of each other where O is the null matrix of the same order as that of A and B. Note: and
cancellation laws hold good.
