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.
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)