Find the inverse of \( A = \left [ \begin{matrix} 4 & 5 & 0 & 0 \\ 3 & 4 & 0 & 0 \\ 0 & 0 & 3 & 2 \\ 0 & 0 & 4 & 3 \end{matrix} \right ] \)

A \( \left [ \begin{matrix} \frac{1}{4} & \frac{1}{5} & 0 & 0 \\ \frac{1}{3} & \frac{1}{4} & 0 & 0 \\ 0 & 0 & \frac{1}{3} & \frac{1}{2} \\ 0 & 0 & \frac{1}{4} & \frac{1}{3} \end{matrix} \right ] \)

B \( \left [ \begin{matrix} \frac{1}{4} & - 5 & 0 & 0 \\ - 3 & \frac{1}{4} & 0 & 0 \\ 0 & 0 & \frac{1}{3} & - 2 \\ 0 & 0 & - 4 & \frac{1}{3} \end{matrix} \right ] \)

C \( \left [ \begin{matrix} 4 & - 3 & 0 & 0 \\ - 5 & 4 & 0 & 0 \\ 0 & 0 & 3 & - 4 \\ 0 & 0 & - 2 & 3 \end{matrix} \right ] \)

D \( \left [ \begin{matrix} 4 & - 5 & 0 & 0 \\ - 3 & 4 & 0 & 0 \\ 0 & 0 & 3 & - 2 \\ 0 & 0 & - 4 & 3 \end{matrix} \right ] \)

Solution

Correct Answer: Option D

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