DRDO CSE 2022 Paper 1 | Question: 1

Question

Compute $\left[M M^{T}\right]^{-1}$ for an orthogonal matrix where

\[M=\left[\begin{array}{lll}
\frac{1}{\sqrt{2}} & \frac{2}{\sqrt{2}} & \frac{-2}{\sqrt{2}} \\
\frac{-2}{\sqrt{2}} & \frac{2}{\sqrt{2}} & \frac{1}{\sqrt{2}} \\
\frac{2}{\sqrt{2}} & \frac{1}{\sqrt{2}} & \frac{2}{\sqrt{2}}
\end{array}\right] .\]

Answer 1

For any orthogonal matrix $$AA^{T} = I$$

And for Identity matrix $$I^{-1} = I$$

$$\therefore\,[MM^{t}]^{-1}=I$$