If $A = \begin{bmatrix} 0 & \sin \alpha \ \sin \alpha & 0 \end{bmatrix}$ and $\det(A^{2} - \frac{1}{2}I) = 0$, then a possible value of $\alpha$ is

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Aicharya · Accepted Answer

A 2 = sin 2 &#945; I So, A 2 - I 2 = sin 2 &#945; - 1 2 2 = 0 &#8658; sin &#945; = 1 2 &#8658; &#945; = &#960; 4

If $A = \begin{bmatrix} 0 & \sin \alpha \\ \sin \alpha & 0 \end{bmatrix}$ and $\det(A^{2} - \frac{1}{2}I) =…