4 3  Properties of matrix addition
The addition of matrices satisfy the following properties:
(i)
Commutative Law  If A = [aij], B = [bij] are matrices of the same order, say
m × n, then A + B = B + A Now
A + B = [aij] + [bij] = [aij + bij]
= [bij + aij] (addition of numbers is commutative)
= ([bij] + [aij]) = B + A
(ii)
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) Now
(A + B) + C = ([aij] + [bij]) + [cij]
= [aij + bij] + [cij] = [(aij + bij) + cij]
= [aij + (bij + cij)]
(Why