I'm very much stuck up on these three problems (and they're the only problems I haven't been able to solve). Anyways, here they are:
1.) If A and B are nonsingular N x N matrices and C = AB, show that C^-1 = (A^-1)(B^-1).
Hint: You must use the associative property of matrix multiplication.
PS: For reference, the associative property of matrix multiplication is A(BC) = (AB)C
2.) Let A be an M x N matrix and B be an N x P matrix.
(a) How many multiplications are needed to calculate AB?
(b) How many additions are needed to calculate AB?
3.) Find (X)(X^T) and (X^T)(X), where X = (1,-1,2).
Note: X^T is the transpose of X.
Any help would be very very very much appreciated. I'm so desperate!