Matrices and Determinants
Properties of Determinants
IIT-JEE 2013
Grade 12
Question:
If $A$ is a $3 \times 3$ matrix with $|A| = 2$, then the value of $|3A|$ is:
(1) $18$
(2) $6$
(3) $24$
(4) $54$
Step-by-Step Solution
Key Concept: Use the scalar-multiplication rule for determinants of an $n \times n$ matrix, $|kA| = k^n|A|$, with $k = 3$ and $n = 3$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (4)