I need to set up a proof for this problem:
Given that $A$ and $B$ are both $n\times n$ matrices. $A$ is invertible, and $AB=BA$.
Prove that $A^{-1}B=BA^{-1}$.
I'm just unsure how to go about this particular proof.
I need to set up a proof for this problem:
Given that $A$ and $B$ are both $n\times n$ matrices. $A$ is invertible, and $AB=BA$.
Prove that $A^{-1}B=BA^{-1}$.
I'm just unsure how to go about this particular proof.