Solution We have
A =
[
]
2
4 , B
1
3
6
5
−



=
−






then
AB =
[
]
2
4
1
3
6
5
−



−






 = 
2
6
12
4
12
24
5
15
30
−
−




−




−


Now
A′ = [–2 4 5] , 
1
B
3
6




′ = 


−

B′A′ =
[
]
1
2
4
5
3
2
4
5
6
12
15
(AB)
6
12
24
30
−








′
−
= −
=








−
−
−




Clearly
(AB)′ = B′A′
3 6  Symmetric and Skew Symmetric Matrices
Definition 4 A square matrix A = [aij] is said to be symmetric if A′ = A, that is,
[aij] = [aji] for all possible values of i and j For example 
3
2
3
A
2
1 5
1
3
1
1




=
−
−




−


 is a symmetric matrix as A′ = A
Definition 5 A square matrix A = [aij] is said to be skew symmetric matrix if
A′ = – A, that is aji = – aij for all possible values of i  and j