)
Therefore
BA = AB
Conversely, if AB = BA, then we shall show that AB is symmetric Now
(AB)′ = B′A′
= B A (as A and B are symmetric)
= AB
Hence AB is symmetric Example 25 Let 
2
1
5
2
2
5
A
, B
, C
3
4
7
4
3
8
−






=
=
=











 Find a matrix D such that
CD – AB = O