)
= [aij] + [(bij + cij)] = [aij] + ([bij] + [cij]) = A + (B + C)
Rationalised 2023-24
MATRICES         47
(iii)
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 (iv)
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