Question

If \(B\) is the inverse of \(A\), which statement must also be true?

Options

• \(A\) is also the inverse of \(B\).

• \(B\) is the identity matrix.

• \(A\) does not possess an inverse.

• \(A\) is a rectangular matrix.

Answer 1

If \(B=A^{-1}\), then \(AB=BA=I\). These same two equalities show that \(A\) is the inverse of \(B\), so \(A=B^{-1}\).