Question

matrix a is such that a^2=2a-i where i is the identity matrix then for​

Answer 1

Given, A  

2

=2A−I              ...(i)

On multiplying by A both sides, we get

A  

2

⋅A=(2A−I)A

⇒A  

3

=2A  

2

−IA

=2(2A−I)−IA  [from equation (i)]

=4A−2I−A         .....(∵IA=A)

=3A−2I

Similarly, A  

4

=4A−3I

⇒A  

5

=5A−4I

Hence, A  

n

=nA−(n−1)I