# Homework Help: Matrix Determinant Question

1. Oct 10, 2009

### ~Sam~

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

Let A, B and C be 3 x 3 invertible matrices where det A = -2 ,det B = -2 and det C is some non-zero scalar.

Then det (CTA−1B2C−1) = ?

and det [ −2(A2)TC2B−1(C−1)2] = ?

the T represents transpose and the -1 represents inverse.

2. Relevant equations

What does the non-zero scalar mean?

3. The attempt at a solution

I used the rule to expand the products of the determinants, but I'm not sure what to do next and what it means by non-zero scalar.

2. Oct 10, 2009

### calimechengr

When you find the determinant of a matrix, your result is a scalar, or a single number. Non zero just means that det(c) is a scalar other than zero.

3. Oct 10, 2009

### ~Sam~

So how would it affect my answer since I really don't know the value of det(c).

4. Oct 10, 2009

### Staff: Mentor

Do you know any theorems about determinants? One that I remember is that det(AT) = det(A). You'll need some of these theorems in these problems, particularly one for det(A-1) as it relates to det(A), and one for det(An) as it relates to det(A).

Tip: To make exponents (for transposes and matrix inverses), click the Go Advanced button below the text entry field. This opens a menu of buttons you can use to format what you write. The X2 button can be used for exponents and the X2 button can be used for subscripts.

a) det(CTA−1B2C−1)
b) det( −2(A2)TC2B−1(C−1)2)

5. Oct 11, 2009

### HallsofIvy

For these problems the most crucial thing you need to know is that det(AB)= det(A)det(B). If you know that, these problems are easy. If you don't, ---.