We now consider some examples Example 3 Show that if
 A = 
cos
sin
sin
cos
θ
θ




−
θ
θ

 , then   An =
cos
sin
sin
cos
n
n
n
n
θ
θ




−
θ
θ


Solution We have
P(n) : An =
cos
sin
sin
cos
n
n
n
n
θ
θ




−
θ
θ


We note that
P(1) : A1 =
cos
sin
sin
cos
θ
θ




−
θ
θ


Therefore, P(1) is true Assume that P(k) is true, i e