P is a non-singular matrix and A, B are two matrices such that `B=P^(-1) AP`. The true statements among the following are

If B is a non singular matrix and A is a square matrix such that B^-1 AB exists, then det (B^-1 AB) is equal to

Define a relation R over a class of n xx n real matrices A and B as ARB iff there exists a non-singular matrix P such that A=P^(-1)BP Then which of the following is true?

if A and B are non-singular matrices ,then

If A is a non singular square matrix, then the false statement among the following is

If matrix A=[[1,22,1]] and a non-singular matrix P=[[-1,1a,b]] is such that P^(-1)AP=diag(-1,3), then the sum of all the elements of A^(100) is

If A and B are non-singular matrices, then

If P is non-singular matrix, then value of adj (P^(-1)) in terms of P is

If A, B are two non-singular matrices of same order, then