Question

Given \[\mathbf{A}=\begin{bmatrix}2&3\\1&2\end{bmatrix}\] and \[\mathbf{B}=\begin{bmatrix}2&-3\\-1&2\end{bmatrix}\], if \[\mathbf{A}\mathbf{B}=\mathbf{B}\mathbf{A}=I\], which statement is correct?

विकल्प

• \[\mathbf{A}\] and \[\mathbf{B}\] are rectangular matrices

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

• \[\mathbf{B}=\mathbf{A}\] and \[\mathbf{A}=\mathbf{B}\]

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

Answer 1

Because both products equal the identity matrix, \(\mathbf{B}\) is the inverse of \(\mathbf{A}\). Likewise, \(\mathbf{A}\) is the inverse of \(\mathbf{B}\).