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