KCET · Maths · Matrices
If \(A\) is a matrix of order \(3 \times 3\), then \(\left(A^2\right)^{-1}\) is equal to
- A \(\left(-A^2\right)^2\)
- B \(\left(A^{-1}\right)^2\)
- C \(A^2\)
- D None of these
Answer & Solution
Correct Answer
(B) \(\left(A^{-1}\right)^2\)
Step-by-step Solution
Detailed explanation
\(\left(A^2\right)^{-1}=(A)^{-2}=\left(A^{-1}\right)^2=\left(-A^{-1}\right)^2=(-A)^{-2}\)
\[
\left(A^2\right)^{-1} \neq A^2,\left(-A^2\right)^2
\]
\[
\left(A^2\right)^{-1} \neq A^2,\left(-A^2\right)^2
\]
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