If the matrices, A, B and `(A+B)` are non-singular, then prove that `[A(A+B)^(-1) B]^(-1) =B^(-1)+A^(-1)`.

Explanation

To prove that \([A(A+B)^{-1} B]^{-1} = B^{-1} + A^{-1}\), we will start by manipulating the left-hand side of the equation step by step.

### Step-by-Step Solution:

1. **Start with the left-hand side:**
\[ LHS = [A(A+B)^{-1} B]^{-1} \]
...