Determinants of a matrix

1. Oct 25, 2007

JFonseka

1. The problem statement, all variables and given/known data
A 2 x 2 matrix B satisfies

B (3 1)$$^{T}$$ = B (5 2)$$^{T}$$

What is det (B) ? Give a reason

2. Relevant equations

None really

3. The attempt at a solution

I really have no idea how to start solving this. Does it involve inversing?

2. Oct 25, 2007

Dick

You are saying Bx=By. What's B(x-y)? Does that give you a hint?

3. Oct 25, 2007

JFonseka

So, It's B(-2 -1)$$^{T}$$

I don't get it though. That doesn't look like a determinant.

4. Oct 25, 2007

Dick

It's also equal to zero since Bx=By. It's not a determinant. But Bz=0 where z is a nonzero vector. What can that tell you about the determinant of B?

5. Oct 25, 2007

JFonseka

That the determinant is 0 ?

6. Oct 25, 2007

Dick

Yessssss.

7. Oct 25, 2007

JFonseka

How do we know B(x) = 0?

8. Oct 25, 2007

JFonseka

Ah nvm I see.

Thanks for the help