If A = 0 sin α sin α 0 and det A 2 - 1 2 I = 0 , then a possible value of α is

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Question: Answered & Verified by Expert

If

A = [\begin{matrix} 0 & \sin α \\ \sin α & 0 \end{matrix}]

and

\det (A^{2} - \frac{1}{2} I) = 0,

then a possible value of

α

is

MathematicsMatricesJEE MainJEE Main 2021 (17 Mar Shift 1)

Options:

A $\frac{π}{2}$
B $\frac{π}{3}$
C $\frac{π}{4}$
D $\frac{π}{6}$

Solution:

2519 Upvotes Verified Answer

The correct answer is:

\frac{π}{4}

$A^{2} = \sin^{2} α I$

So, $|A^{2} - \frac{I}{2}| = {(\sin^{2} α - \frac{1}{2})}^{2} = 0$

$\Rightarrow \sin α = \frac{1}{\sqrt{2}}$

$\Rightarrow α = \frac{π}{4}$

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