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JEE Main · 2026 · 24 Jan 2026 · Shift 2 · Matrices

Let

P = [p_{ij}]

and

Q = [q_{ij}]

be two square matrices of order 3 such that

q_{ij} = 2^{(i + j - 1)} p_{ij}

and

det (Q) = 2^{10}

. Then the value of

det (adj (adj P))

is :

(A)32
(B)16✓ Correct
(C)81
(D)124

Answer: (B)

Solution

Writing

q_{ij} = 2^{i} 2^{j - 1} p_{ij}

, a factor

2^{i}

comes out of row

i

and

2^{j - 1}

out of column

j

, so

det Q = 2^{(1 + 2 + 3)} 2^{(0 + 1 + 2)} det P = 2^{9} det P

. With

det Q = 2^{10}

this gives

det P = 2

. For a

3 \times 3

matrix

det (adj (adj P)) = (det P)^{(n - 1)^{2}} = (det P)^{4} = 2^{4} = 16

.

JEE Main · 2026 · 24 Jan 2026 · Shift 2 · Single correct option

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