Question

If $A = \frac{1}{7} \begin{bmatrix} 3 & -2 & 6 \\-6 & -3 & 2 \\ -2 & 6 & 3 \end{bmatrix}$, then $A^{-1} = $ ?

• A. $A^{-1} = A$
• B. $A^{-1} = A^T$
• C. $A^{-1}$ does not exist
• D. $A^{-1} = -A$

Hint:

A matrix $A$ is orthogonal if $A^{-1} = A^T$, i.e., $AA^T = I$.

Answer 1

The Correct Option is B

If $A^{-1} = A^T$, then $A$ is orthogonal. To verify, check $AA^T = I$ for given matrix.
Calculation confirms $A$ is orthogonal $\Rightarrow A^{-1} = A^T$