GATE 2018 CE (CE1) – Question 12
Engineering Mathematics · Linear Algebra: Matrix algebra, systems of linear equations, eigenvalues and eigenvectors · 1 mark · Multiple choice
Find the inverse of the orthogonal matrix $$Q=\frac17\begin{bmatrix}3&2&6\\-6&3&2\\2&6&-3\end{bmatrix}$$.
- $$\frac17\begin{bmatrix}3&2&6\\-6&3&2\\2&6&-3\end{bmatrix}$$
- $$\frac17\begin{bmatrix}-3&-2&-6\\6&-3&-2\\-2&-6&3\end{bmatrix}$$
- $$\frac17\begin{bmatrix}3&-6&2\\2&3&6\\6&2&-3\end{bmatrix}$$
- $$\frac17\begin{bmatrix}-3&6&-2\\-2&-3&-6\\-6&-2&3\end{bmatrix}$$
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Correct answer: (C) $$\frac17\begin{bmatrix}3&-6&2\\2&3&6\\6&2&-3\end{bmatrix}$$
Explanation
An orthogonal matrix obeys $Q^TQ=I$, hence $Q^{-1}=Q^T$. Transpose the rows and columns of Q to obtain option C.