Invertible Matrices

If A is an invertible matrix and B is a matrix, then

If A and B are two invertible square matrices of same order, then what is (AB)^(-1) equal to ?

Consider the following relation R on the set of realsquare matrices of order 3. R = {(A, B)| A = P^-1 BP for some invertible matrix P} Statement I R is an equivalence relation. Statement II For any two invertible 3xx3 matrices M and N, (MN)^-1 = N^-1 M^-1

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

If A is an invertible square matrix then |A^(-1)| =?

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

A and B are square matrices of same order such that A^5=B^5 and A^2B^3=B^2A^3 . If A^2-B^2 invertible then det(A^3+B^3)=?

For a function to be invertible it must be

Is every invertible function monotonic?