Answer to Question #52680 in Linear Algebra for ravish

Question

For the following matrices, check whether the reexists an invertible matrix P such that P−1 A Pis diagonal. When such a P exists,find P.
i)A=( 0 1 -3)
( 2 -1 6)
( 1 -1 4)
(ii) B is equal to. ( 0 0 -2)
( 1 2 1)
( 1 0 3)

b)Find the inverse of the matrix B in part (a) by using Cayley-Hamilton theorem.(3)c)Using the fact that det(AB)=det(A)det(B)for any two matrices A and B,prove the identity (a2+b2) (c2+d2)=(ac−bd)2+(ad+bc)2