Question

Which multiplication is performed on \[B(AB)^{-1}=A^{-1}\] to obtain \[I(AB)^{-1}=B^{-1}A^{-1}\]?

Options

• Pre multiplying both sides by \[A^{-1}\]

• Pre multiplying both sides by \[B^{-1}\]

• Post multiplying both sides by \[A^{-1}\]

• Post multiplying both sides by \[B^{-1}\]

Answer 1

Pre multiplying by \(B^{-1}\) gives \(B^{-1}B(AB)^{-1}=B^{-1}A^{-1}\). Since \(B^{-1}B=I\), it follows that \((AB)^{-1}=B^{-1}A^{-1}\).