If \( A \) is an orthogonal matrix, then \( A^{-1} \) is
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- Symmetric
- Skew-symmetric
- Orthogonal
- Hermitian
The Correct Option is C
Solution and Explanation
We are given that \( A \) is an orthogonal matrix. By definition, a matrix \( A \) is orthogonal if:
\[ A^T A = A A^T = I \]
Where \( I \) is the identity matrix. The inverse of an orthogonal matrix is also orthogonal. Specifically, for an orthogonal matrix \( A \), we have:
\[ A^{-1} = A^T \]
This means the inverse of an orthogonal matrix is also orthogonal, as its transpose is its inverse.
Thus, the correct answer is option (C), Orthogonal.
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