Let A and B be matrices of order n. Prove that if
(I - AB) is invertible, (I - BA) is also invertible and
`(I-BA)^(-1) = I + B (I- AB)^(-1)A, ` where I be the identity matrix
of order n.

Explanation

To prove that if \( (I - AB) \) is invertible, then \( (I - BA) \) is also invertible, and that \( (I - BA)^{-1} = I + B (I - AB)^{-1} A \), we will follow these steps:

### Step 1: Show that if \( (I - AB) \) is invertible, then \( (I - BA) \) is also invertible.

Assume \( (I - AB) \) is invertible. This means that there exists a matrix \( C \) such that:

\[
(I - AB)C = I
...