Let $A$ and $B$ be $n$ x $n$ matrices over reals. Show that $I - BA$ is invertible if $I - AB$ is invertible. Deduce that $AB$ and $BA$ have the same eigenvalues.
I know how to prove that $AB$ and $BA$ have same eigen values, when either $A$ or $B$ is non-singular.
But here, that condition is not mentioned.
Please help me.