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KCET · Maths · Matrices

If \(A\) is a matrix of order \(3 \times 3\), then \(\left(A^2\right)^{-1}\) is equal to

  1. A \(\left(-A^2\right)^2\)
  2. B \(\left(A^{-1}\right)^2\)
  3. C \(A^2\)
  4. D None of these
Verified Solution

Answer & Solution

Correct Answer

(B) \(\left(A^{-1}\right)^2\)

Step-by-step Solution

Detailed explanation

\(\left(A^2\right)^{-1}=(A)^{-2}=\left(A^{-1}\right)^2=\left(-A^{-1}\right)^2=(-A)^{-2}\)
\[
\left(A^2\right)^{-1} \neq A^2,\left(-A^2\right)^2
\]