JEE Advanced · 2017 · 21 May 2017 · Paper 1 · Matrices

If $A$ is a real matrix, then $|A^2|=|A{|}^2\ge 0$. For option (B): determinant is $-1<0$, so it cannot be $A^2$. For option (D): determinant is $-1<0$, so it cannot be $A^2$. Option (A) is the identity matrix $I=I^2$. Option (C) has determinant $1>0$ and equals ${\left[\begin{array}{ccc}1& 0& 0\\ 0& 0& 1\\ 0& -1& 0\end{array}\right]}^2$.