Hi all.

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.) IfAandBare nonsingularNxNmatrices andC = AB, show thatC^-1=(A^-1)(B^-1).

Hint: You must use the associative property of matrix multiplication.

PS: For reference, the associative property of matrix multiplication isA(BC) = (AB)C

2.) LetAbe anMxNmatrix andBbe anNxPmatrix.

(a) How many multiplications are needed to calculateAB?(b) How many additions are needed to calculate

AB?

3.) Find(X)(X^T)and(X^T)(X), whereX= (1,-1,2).

Note: X^Tis the transpose ofX.

Any help would be very very very much appreciated. I'm so desperate!