Question

If \(B\) satisfies \[AB=BA=I\] for a square matrix \(A\), what is \(B\) called and how is it denoted?

Options

• The inverse matrix of \(A\), denoted by \[A^{-1}\]

• The inverse matrix of \(B\), denoted by \[B^{-1}\]

• A rectangular matrix, denoted by \[A^{-1}\]

• The identity matrix of \(A\), denoted by \[I^{-1}\]

Answer 1

When \(B\) gives the identity matrix on multiplication with \(A\) from either side, \(B\) is the inverse matrix of \(A\). It is denoted by \(A^{-1}\).