Official PYQ · 2026Set 2 · Q52Linear Algebra: Matrices, Determinants, System of Linear EquationsNAT2 marks

GATE CS 2026 Set 2 Q52 — Linear Algebra: Matrices, Determinants, System of Linear Equations

The determinant of a

4 \times 4

matrix

A

3

. The value of the determinant of

2 A

\_\_\_\_

. (answer in integer)

View worked solution

Answer: 48:48

Using the properties of determinants, for any $n \times n$ matrix $A$ and a scalar $k$ , the determinant of $k A$ is given by:

\det(k A) = k^n \det(A)

Given in the problem:

The size of the matrix $A$ is $4 \times 4$ , so $n = 4$ .
The scalar multiplier is $k = 2$ .
The determinant of $A$ is $\det(A) = 3$ .

Substituting these values into the formula:

\det(2 A) = 2^4 \times \det(A)

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

Thus, the value of the determinant of $2 A$ is 48.

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Published 10 Oct 2026

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