CUET UG 2025 — Mathematics Algebra

2025mcqmedium

If A be a square matrix of order 3 such that $|A| = 2$ , then $|adj(2A)|$ is equal to

Official previous-year question

Held on 3 Jun 2025 · Verified 13 Jul 2026.

Options

A
16
B
32
C
64
D
256

Did you get this right?

Solution

Given that $A$ is a square matrix of order 3 and $|A| = 2$ .

For a matrix of order $n$ , when multiplying by a constant $k$ :

$|kA| = k^n \times |A|$

Here, $k = 2$ and $n = 3$ :

$|2A| = 2^3 \times |A|$

$|2A| = 8 \times 2$

$|2A| = 16$

For any square matrix $B$ of order $n$ :

$|adj(B)| = |B|^{n-1}$

Let $B = 2A$ , where $|2A| = 16$ and $n = 3$ :

$|adj(2A)| = |2A|^{3-1}$

$|adj(2A)| = |2A|^2$

$|adj(2A)| = (16)^2$

$|adj(2A)| = 256$

Therefore, $|adj(2A)| = 256$ .

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CUET UG 2025 — Mathematics Algebra

2025mcqmedium

If A be a square matrix of order 3 such that $|A| = 2$ , then $|adj(2A)|$ is equal to

Official previous-year question

Held on 3 Jun 2025 · Verified 13 Jul 2026.

Options

A
16
B
32
C
64
D
256

Did you get this right?

Solution

Given that $A$ is a square matrix of order 3 and $|A| = 2$ .

For a matrix of order $n$ , when multiplying by a constant $k$ :

$|kA| = k^n \times |A|$

Here, $k = 2$ and $n = 3$ :

$|2A| = 2^3 \times |A|$

$|2A| = 8 \times 2$

$|2A| = 16$

For any square matrix $B$ of order $n$ :

$|adj(B)| = |B|^{n-1}$

Let $B = 2A$ , where $|2A| = 16$ and $n = 3$ :

$|adj(2A)| = |2A|^{3-1}$

$|adj(2A)| = |2A|^2$

$|adj(2A)| = (16)^2$

$|adj(2A)| = 256$

Therefore, $|adj(2A)| = 256$ .

Your note

CUET UG Algebra in other years

Algebra 2026 Algebra 2024 Algebra 2023 Algebra 2022

Keep practicing Algebra

Work through every CUET UG Algebra PYQ, year by year.

Browse all Mathematics topics

CUET UG 2025 — Mathematics Algebra

Options

Did you get this right?

Solution

Your note

CUET UG Algebra in other years

More CUET UG Algebra questions

Other Mathematics topics for CUET UG

Calculus

Applied-Mathematics

Statistics & Applications

Geometry

Arithmetic

Coordinate Geometry

Keep practicing Algebra

CUET UG 2025 — Mathematics Algebra

Options

Did you get this right?

Solution

Your note

CUET UG Algebra in other years

More CUET UG Algebra questions

Other Mathematics topics for CUET UG

Calculus

Applied-Mathematics

Statistics & Applications

Geometry

Arithmetic

Coordinate Geometry

Keep practicing Algebra