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Question: Answered & Verified by Expert
If $A$ is a matrix of order $3 \times 3$, then $\left(A^2\right)^{-1}$ is equal to
MathematicsMatricesKCETKCET 2022
Options:
  • A $\left(-A^2\right)^2$
  • B $\left(A^{-1}\right)^2$
  • C $A^2$
  • D None of these
Solution:
2150 Upvotes Verified Answer
The correct answer is: $\left(A^{-1}\right)^2$
$\left(A^2\right)^{-1}=(A)^{-2}=\left(A^{-1}\right)^2=\left(-A^{-1}\right)^2=(-A)^{-2}$
$$
\left(A^2\right)^{-1} \neq A^2,\left(-A^2\right)^2
$$

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