GATE CS 2026 Set 2 Q.62: Linear Algebra

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

Your answer

Official answer and solution

Solution

Use the determinant scaling property $\det(kA) = k^n \det(A)$ for an $n \times n$ matrix.

For any $n \times n$ matrix $A$ and scalar $k$ , $\det(kA) = k^n \det(A)$ . Here $n = 4$ , $k = 2$ , and $\det(A) = 3$ , so:

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

Final answer

Common trap

Multiplying by 2 instead of $2^4 = 16$ .

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Paper: GATE 2026 Computer Science and Information Technology - Session 2 (CS2)
Question: 62 of 65
Section: Computer Science and Information Technology

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