Solution Since A and B are both symmetric matrices, therefore A′ = A and B′ = B Rationalised 2023-24
MATRICES         71
Let
AB be symmetric, then (AB)′ = AB
But
(AB)′ = B′A′= BA (Why )
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