Question

Starting with \[(AB)(AB)^{-1}=I\], what equation results after pre multiplying both sides by \[A^{-1}\]?

Options

• \[A(AB)(AB)^{-1}=A\]

• \[B^{-1}(AB)(AB)^{-1}=B^{-1}\]

• \[(AB)(AB)^{-1}A^{-1}=A^{-1}\]

• \[A^{-1}(AB)(AB)^{-1}=A^{-1}\]

Answer 1

Pre multiplying means multiplying on the left side of each member by \(A^{-1}\). Therefore the resulting equality is \(A^{-1}(AB)(AB)^{-1}=A^{-1}\).