|Class 12 Maths Matrices||Properties of Matrix Addition|
Properties of Matrix Addition
Commutative Law : If A = [aij], B = [bij] are matrices of the same order, say m × n, then A + B = B + A.
Associative Law : For any three matrices A = [aij], B = [bij], C = [cij] of the same order, say m × n, (A + B) + C = A + (B + C).
Existence of additive identity : Let A = [aij] be an m × n matrix and O be an m × n zero matrix, then A + O = O + A = A. In other words, O is the additive identity for matrix addition.
The existence of additive inverse : Let A = [aij]m × n be any matrix, then we have another matrix as – A = [– aij]m × n such that A + (– A) = (– A) + A= O. So – A is the additive inverse of A or negative of A.