Question

The matrix having the same matrix as its inverse is:

• A. $\left[\begin{array}{ccc}1& 1& 1\\ 1& 1& 1\\ 1& 1& 1\end{array}\right]$
• B. $\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$
• C. $\left[\begin{array}{ccc}1& 0& 1\\ 0& 0& 0\\ 1& 0& 1\end{array}\right]$
• D. $\left[\begin{array}{ccc}0& 1& 0\\ 1& 1& 1\\ 0& 1& 0\end{array}\right]$

Answer 1

The correct option is B $\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$

An inverse $A$ of a matrix $M$ is one such that $AM=MA=I$.

For the identity matrix $M=I$, this means $AI=IA=I.$ Note that the identity is the unique matrix I such that $IM=MI=I,$ so letting $M$ here take the place of I, the only matrix inverse $A$ satisfying this relation is also $I$.

hence option B is correct