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MARCH 2024 — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsMARCH 20242 Marks
Question
Check whether the following matrix is invertible or not:$
\left[\begin{array}{cc}
\cos \theta & \sin \theta \\
-\sin \theta & \cos \theta
\end{array}\right]
$
✓

Answer

Let $A=\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right]$
Then, $|A|=\left|\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right|=\cos ^2 \theta+\sin ^2 \theta=1 \neq 0$
$\therefore A$ is a non-singular matrix.
Hence, A is invertible.

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