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JEE Main · 2024 · 04 Apr 2024 · Shift 1 · Determinants

Let

α \in (0, \infty)

and

A = 110201 α 12

. If

det (adj (2 A - A^{T})) = 2^{8}

, then

(det (A))^{2}

is equal to

(A)16✓ Correct
(B)36
(C)49
(D)1

Answer: (A)

Solution

For a

3 \times 3

matrix,

det (adj M) = (det M)^{2}

. From

det (adj (2 A - A^{T})) = 2^{8}

,

(det (2 A - A^{T}))^{2} = 2^{8} \Rightarrow det (2 A - A^{T}) = \pm 16.

Computing

2 A - A^{T}

and imposing this determinant gives

α = 1

. Then

det A = 110201112 = - 4, (det A)^{2} = 16.

Option A.

JEE Main · 2024 · 04 Apr 2024 · Shift 1 · Single correct option

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