If AB = I or BA= I, then prove that A is invertible and `B=A^(-1)`.

If A+B=45^(@) , then prove that (i) (1+ tan A) (1+ tan B) =2 (ii) (cot A-1) (cot B-1)=2

If A and B are square matrices of the same order such that AB = BA, then prove by induction that AB^(n)=B^(n)A . Further, prove that (AB)^(n)=A^(n)B^(n) for all n in N .

If A is an invertible matrix and A is also invertible then prove (A^(T))^(-1) = (A^(-1))

If f:A to B is a bijective function then prove that (ii) f^(-1) of =I_(A) .

If A and B are symmetric matrices of the same order, then show that AB is symmetric if and only if A and B commute, that is AB = BA.

If [(a,b),(c,d)] is invertible then