# Homework Help: Determinate Algebra Question

1. Oct 18, 2009

### Whiz

1. The problem statement, all variables and given/known data

If A and B are 3 x 3 matrices satisfying det(2A(B^-1)) = -20 and det((A^2)(B(transpose))) = 50, find det(A) and det(B)

2. Relevant equations

None

3. The attempt at a solution

I'm not quite sure how to do the question at all. I've just been guessing the determinants and seeing if it satisfies the two equations. I found that det(A) = -5 and det(B) = 2, but I just guessed.

How can I work this out?

Last edited: Oct 18, 2009
2. Oct 18, 2009

### HallsofIvy

Use the facts that det(AB)= det(A)det(B), and that det(A transpose)= det(A) so that 2det(A)/det(B)= -20 and (det(A)2)det(B)= 50 so that you have two equations to solve for det(A) and det(B). (And det(A)= -5, det(B)= 2 is not correct. 2(-5)/(2)= -5, not -20.)

Can you solve 2x/y= -20 and x2y= 50?

And, the word is "determinant", not "determinate".

3. Oct 18, 2009

### Whiz

Thanks for the quick reply.

I'm not sure that's how you solve this question because the answer in the book is det(A) = 5 and det(B) = 2, which would make my answer wrong as well.