Q34Section B (Section B)34 of 60

Orthogonal completion of a two-by-two matrix

For real constants $a$ and $b$ , let $M=\begin{pmatrix}\dfrac{1}{\sqrt{2}}&\dfrac{1}{\sqrt{2}}\\a&b\end{pmatrix}$ be an orthogonal matrix. Then which of the following statements is/are always TRUE?

Multiple select: one or more options are correct. Select all of them, then submit — marks need the exact set.

Select every correct option, then submit.

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