Question

If \(A\) is invertible, which pair of equations must \[A^{-1}\] satisfy?

पर्याय

• \[AA^{-1}=0\] and \[A^{-1}A=0\]

• \[AA^{-1}=A\] and \[A^{-1}A=A\]

• \[AA^{-1}=I\] and \[A^{-1}A=I\]

• \[AA^{-1}=A^{-1}\] and \[A^{-1}A=A^{-1}\]

Answer 1

The inverse of \(A\) must produce the identity matrix regardless of the multiplication order. Thus, both \(AA^{-1}\) and \(A^{-1}A\) are equal to \(I\).