If A and B are symmetric non singular matrices, AB = BA and `A^(-1) B^(-1)` exist, then prove that `A^(-1)B^(-1)` is symmetric.

If A and B are two square matrices such that B = - A^(-1) BA then (A + B)^(2) is equal to

Suppose A and B are two symmetric matrices. Prove that (AB)^T = BA

If A and B are symmetric matrices, prove that A B-B A is a skew symmetric matrix.

A and B are two non - singular matrices such that A^(6) = I and AB^(2) = BA( B != I) . A value of k so that B^(k) = I is a)31 b)32 c)64 d)63

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

If A and B are symmetric matrices of the same order, then prove that (A+B) is also symmetric.

Consider the matrix A = [(1,2,1),(0,1,2),(-1,1,4)] Find A A^T and hence prove that A A^T is symmetric.

If A is an 3 xx 3 non - singular matrix such that AA'= A'A and B = A^(-1) A' , then BB' equals a)I + B b)I c) B^(-1) d) (B^(-1))

Let A and B are two square matrices such that AB = A and BA = B , then A ^(2) equals to : a)B b)A c)I d)O

If A+B=45^(circ) , prove that (cot A-1)(cot B-1) = 2