The determinant of a 4 × 4 matrix A is 3. The value of the determinant of 2A is … (answer in integer)

Linear Algebra

GATE CSE 2026 Set 2 · Q62

NAT2 marksEasy

Time00:00

The determinant of a $4 \times 4$ matrix $A$ is $3$ . The value of the determinant of $2A$ is __________. (answer in integer)

Your answerNumerical answer

Enter a value to check

Solution

Step-by-step verified solution

Official answer: 48

Linear Algebra

For any $n \times n$ square matrix $A$ and a scalar $c$ , the determinant of $cA$ satisfies the property:

\det(cA) = c^n \det(A)

Given:

Matrix dimension: $n = 4$
Scalar: $c = 2$
$\det(A) = 3$

Substituting these values:

\det(2A) = 2^4 \times \det(A) = 16 \times 3 = 48

Try the question first, then check your work.

Think the official key or this write-up is wrong?

Report error or challenge

Examiner trap

The misconception this question tests

This Linear Algebra previous year question is Q62 of the GATE CSE 2026 Set 2 paper. Find more GATE CSE PYQs on Linear Algebra in Engineering Mathematics, or browse all GATE CSE PYQs.

Free diagnostic

Where do you stand for GATE?

Take the 20-minute diagnostic: the 3 topics that cost you the most marks, and a rank range. Or sit 5 related Linear Algebra PYQs now with no account.

One GATE CSE PYQ every morning

An official question by email at 7 AM IST, with a link to its verified solution. Unsubscribe in one click.

Linear Algebra in GATE CSE

Linear Algebra has 46 GATE CSE PYQs across 26 papers from 2011 to 2026. 4 of them are 2-mark NAT questions like this one, and GATE CSE 2026 Set 2 has 2.

How GATE tests Linear Algebra

More from GATE CSE 2026 Set 2

Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.