If `A=[[2,3],[1,-4]]`and `B=[[1,-2],[-1,3]]`, then verify that `(A B)^(-1)=B^(-1)A^(-1)`

Explanation

To verify that \((AB)^{-1} = B^{-1}A^{-1}\) for the matrices \(A\) and \(B\), we will follow these steps:

1. **Calculate the product \(AB\)**.
2. **Find the inverse of \(AB\)** using the formula \((X)^{-1} = \frac{1}{\text{det}(X)} \cdot \text{adj}(X)\).
3. **Calculate the inverse of \(A\)**.
4. **Calculate the inverse of \(B\)**.
5. **Calculate the product \(B^{-1}A^{-1}\)**.
6. **Compare \((AB)^{-1}\) with \(B^{-1}A^{-1}\)**.
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