Solution We have
2A – B = 2 1
2
3
2
3 1
3
1
3
1
0
2



 −
−
−




=
2
4
6
3 1
3
4
6
2
1
0
2
−
−




+



−




=
2
3
4
1
6
3
1
5
3
4
1
6
0
2
2
5
6
0
−
+
−
−




=




+
+
−




3 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)