Question

If \(A\) and \(B\) are invertible matrices of the same order, which expression is the inverse of \(AB\)?

Options

• \[(AB)^{-1}=AB\]

• \[(AB)^{-1}=BA\]

• \[(AB)^{-1}=B^{-1}A^{-1}\]

• \[(AB)^{-1}=A^{-1}B^{-1}\]

Answer 1

The inverse of a product is obtained by taking the inverses in reverse order. Hence the inverse of \(AB\) is \(B^{-1}A^{-1}\), not \(A^{-1}B^{-1}\).