Thus by principle of mathematical induction,
we have 
cos
sin
A
sin
cos
n
n
n
n
n
θ
θ


= 

−
θ
θ


, holds for all natural numbers Example 24 If A and B are symmetric matrices of the same order, then show that AB
is symmetric if and only if A and B commute, that is AB = BA 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