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Question: Answered & Verified by Expert
If $A=\left[\begin{array}{cc}i & 0 \\ 0 & -i\end{array}\right]$, $B=\left[\begin{array}{ll}0 & i \\ i & 0\end{array}\right]$
where $i=\sqrt{-1}$, then the correct relation is
MathematicsMatricesJEE Main
Options:
  • A $A+B=0$
  • B $A^2=B^2$
  • C $A-B=0$
  • D $A^2+B^2=0$
Solution:
1804 Upvotes Verified Answer
The correct answer is: $A^2=B^2$
Relation $A^2=B^2$ is true because $A^2=\left[\begin{array}{cc}-1 & 0 \\ 0 & -1\end{array}\right]$ and $B^2=\left[\begin{array}{cc}-1 & 0 \\ 0 & -1\end{array}\right]$ have same matrices.

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