Question

Help with matrix problem : find the determinant given that A isa 3x3 matrix for which det(A)=-3

(a) det(3A^T) (b) det(2A^-1)

Answer 1

Okay, det(A) = -3, what's det(A^T) ?

Answer 2

No, that's the problem. Those are the only given.

Answer 3

I'm confused on what's supposed to do. lol

Answer 4

Yes, but you should know these two properties by heart, ok? Read carefully...
\[\large \det(A^T) = \det(A)\][Transposes have the same determinant]

\[\large \det(A^{-1}) = \frac1{\det(A)}\]

Answer 5

So, does it mean that that the answer is just for (a) is 3(-3)?

Answer 6

Or am I getting it wrong?

Answer 7

No... it isn't that simple, I'm afraid... but it IS still rather simple...
Here's another property:
\[\Large \det(cA) = c^n\det(A)\]
Where n is the dimension of the matrix A.

Answer 8

So how do I actually do it? Can you show me an example. Help me with (a).

Answer 9

Certainly :)
\[\Large \det(3A^T) = 3^3 \det(A^T)\] right?

Answer 10

Wait, so the size of the matrix is 3x3, right? So how do I get 3 as the exponent?

Answer 11

BECAUSE it's a 3x3 matrix :)
If it was 4x4, the exponent would be 4 :D

Answer 12

I mean, how to solve for it, like you get it. Haha

Answer 13

I have a question, what if it's a 2x3? Haha

Answer 14

You're being silly... non-square matrixes don't even have determinants :D

Answer 15

Oooh. I don't know that. Hahaha

Answer 16

Ok, back to the problem.

Answer 17

\[\Large \det(3A^T) = 3^3 \det(A^T)\]
You can work from here, you know the determinant of A^T, and you know 3^3

Answer 18

Ok thanks! Sorry man for late replies, I'm running errands. thanks!