I don't understand this invertible problem?

Hello all, this was on my practice final exam for my linear algebra class.

Let A and B be two nxn square matricies such that AB is invertible. Prove that homogeneous equation (A^2)x=0 Hint:show that A must be invertible,

The only thing I know is that since A is invertible, by the Inverible MAtrix Theorem, Ax=0 has only trivial solution.

Help!!

Re: I don't understand this invertible problem?

Re: I don't understand this invertible problem?

This question was before we had learned about determinants. I don't think the professor will allow us to use the determinant to prove it.

That being said the determinant of a product, for example:

det(AB) will be equal to det(A) x det(B)

Re: I don't understand this invertible problem?

Quote:

Originally Posted by

**elpermic** This question was before we had learned about determinants. I don't think the professor will allow us to use the determinant to prove it.

That being said the determinant of a product, for example:

det(AB) will be equal to det(A) x det(B)

So if , what can you say about and ?

Re: I don't understand this invertible problem?

since detA and detB aren't 0, then A is invertible. And A^k is invertible for any k

Re: I don't understand this invertible problem?

Re: I don't understand this invertible problem?

Alright thank you very much!

I just hope that I can do well on my final :/

Re: I don't understand this invertible problem?