Can someone help me out with this identity?
We are given two matrices $A$ and $B$. The matrix $A$ is $m\times n$ while $B$ is $n\times m$ matrix. We need to prove that
$\det(I+AB) = \det(I + BA)$ where $I$ is the corresponding identity matrix.
Please use elementary steps to solve as I don't have enough knowledge of matrices.
I checked out the Sylvester's determinant identity page in maths stack exchange. The proofs were out of my scope. Can it be done in an easier way?
