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TIFR QUESTION 2023

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the properties of an orthogonal matrix :

1. It preserves lengths.

2. It preserves angles

By above properties , Options B and C = False

Now Option A :

If Mx = 0, this means the matrix maps a non-zero vector to the zero vector.

A rotation/reflection cannot do this. If a non-zero vector is rotated, its length
remains the same, so it can't become the zero vector.

An orthogonal matrix is always invertible, and its determinant is non-zero.
The only vector it maps to zero is the zero vector itself.

Conclusion: The statement is False.
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