Question

A square matrix \(A\) of order \(m \times m\) is called invertible (or non-singular) when there exists a square matrix \(B\) of the same order such that which condition holds?

Options

• \[AB=BA=I\]

• \[AB=BA=A\]

• \[AB=A+B=I\]

• \[AB=BA=B\]

Answer 1

An invertible matrix has another square matrix of the same order whose product with it is the identity matrix. The required condition must hold in both orders: \(AB=I\) and \(BA=I\).