Prabhav Dutt

In such questions we should remember the "Cayley-Hamilton"equation which states that: 

"Every square matrix satisfies its own characteristic equation"

For the given matrix A, we first calculate its characteristic equation. 

to calculate the characteristic equation we should remember the method to calculate the characteristic equation of any matrix: 

Latest denote the characteristic equation of matrix A by q(s) 

So, by definition q(s) =  det(sI-A)=0

Here I is the identity matrix of the same order as matrix A

So, Identity matrix I= 

sI= 

So. sI-A = - 

=

So det(sI-A) = (s-3)(s-2)+1=0

-5s +7=0

Now since the above equation is zero and the matrix satisfies cayley Hamilton equation so the matrix must also satisfy the above equation hence we can say that

Hence proved