CUET · MATHS · PYQ PAPER 2025
The inverse of the matrix \(\left[\begin{array}{lll}4 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 6\end{array}\right]\) is
- A \(\left[\begin{array}{ccc}-\frac{1}{4} & 0 & 0 \\ 0 & -\frac{1}{5} & 0 \\ 0 & 0 & -\frac{1}{6}\end{array}\right]\)
- B \(\left[\begin{array}{ccc}-\frac{1}{30} & 0 & 0 \\ 0 & \frac{1}{24} & 0 \\ 0 & 0 & \frac{1}{20}\end{array}\right]\)
- C \(\left[\begin{array}{ccc}\frac{1}{4} & 0 & 0 \\ 0 & \frac{1}{5} & 0 \\ 0 & 0 & \frac{1}{6}\end{array}\right]\)
- D \(\left[\begin{array}{lll}6 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 4\end{array}\right]\)
Answer & Solution
Correct Answer
(C) \(\left[\begin{array}{ccc}\frac{1}{4} & 0 & 0 \\ 0 & \frac{1}{5} & 0 \\ 0 & 0 & \frac{1}{6}\end{array}\right]\)
Step-by-step Solution
Detailed explanation
\( \left[\begin{array}{lll}4 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 6\end{array}\right]^{-1} = \left[\begin{array}{ccc}\frac{1}{4} & 0 & 0 \\ 0 & \frac{1}{5} & 0 \\ 0 & 0 & \frac{1}{6}\end{array}\right] \)
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