COMPASSLearning

Talk to us Register Login

JEE Main · 2022 · 27 Jun 2022 · Shift 2 · Matrices

Let A and B be two

3 \times 3

matrices such that

A B = I

and

∣ A ∣ = \frac{1}{8}

then

∣ adj (B adj (2 A)) ∣

is equal to

(A)16
(B)32
(C)64✓ Correct
(D)128

Answer: (C)

Solution

Since

A B = I

, we have

∣ A ∣∣ B ∣ = 1

. Given

∣ A ∣ = \frac{1}{8}

, so

∣ B ∣ = 8

.

For a

3 \times 3

matrix M,

∣ adj (M) ∣ = ∣ M ∣^{n - 1} = ∣ M ∣^{2}

.

∣ adj (B adj (2 A)) ∣ = ∣ B adj (2 A) ∣^{2} = ∣ B ∣^{2} ∣ adj (2 A) ∣^{2}

∣ adj (2 A) ∣ = ∣2 A ∣^{2} = (2^{3} ∣ A ∣)^{2} = 64∣ A ∣^{2} = 64 \cdot \frac{1}{64} = 1

Therefore,

∣ adj (B adj (2 A)) ∣ = 8^{2} \cdot 1^{2} = 64

.

Answer: (C)

JEE Main · 2022 · 27 Jun 2022 · Shift 2 · Single correct option

Practise more: all JEE Main PYQs on Matrices →

More JEE Main questions on Matrices

For some $α, β \in R$ , let $A = [α 1 22]$ and $B = [11 1 β]$ be such that $A^{2} - 4 A + 2 I = B^{2} - 3 B + I = O$ . Then …
JEE Main 2026View solution →
For the matrices $A = [31 - 4 - 1]$ and $B = [- 29 - 13 4918]$ , if …
JEE Main 2026View solution →
If the system of equations
$3 x + y + 4 z = 3$
$2 x + α y - z = - 3$
$x + 2 y + z = 4$
has no solution, then the value of $α$ is equal to:
JEE Main 2026View solution →
If $A = [2335]$ , then the determinant of the matrix $(A^{2025} - 3 A^{2024} + A^{2023})$ is
JEE Main 2026View solution →
Let A be a $3 \times 3$ matrix such that $A + A^{T} = O$ . If …
JEE Main 2026View solution →
If $X = x y z$ is a solution of the system of equations $A X = B$ , where $adj A = 4 - 5 1 20 - 2 253$ and $B = 402$ , then $∣ x + y + z ∣$ is equal t …
JEE Main 2026View solution →