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AP EAMCET · Maths · Matrices

If \(A=\left[\begin{array}{lll}3 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 4\end{array}\right]\) and \(B=A^3\), then \(B^{-1}=\)

  1. A \(\left[\begin{array}{ccc}-3 & 0 & 0 \\ 0 & -5 & 0 \\ 0 & 0 & -4\end{array}\right]\)
  2. B \(\left[\begin{array}{ccc}-27 & 0 & 0 \\ 0 & -125 & 0 \\ 0 & 0 & -64\end{array}\right]\)
  3. C \(\left[\begin{array}{ccc}\frac{1}{27} & 0 & 0 \\ 0 & \frac{1}{125} & 0 \\ 0 & 0 & \frac{1}{64}\end{array}\right]\)
  4. D \(\left[\begin{array}{ccc}\frac{-1}{27} & 0 & 0 \\ 0 & \frac{-1}{125} & 0 \\ 0 & 0 & \frac{-1}{64}\end{array}\right]\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\left[\begin{array}{ccc}\frac{1}{27} & 0 & 0 \\ 0 & \frac{1}{125} & 0 \\ 0 & 0 & \frac{1}{64}\end{array}\right]\)

Step-by-step Solution

Detailed explanation

The given matrix \(A=\left[\begin{array}{lll}3 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 4\end{array}\right]\) and…