Let $A = [a_{ij}]_{3×3}$ such that $|A| = −5$. Then the value of $\text{det (5A)}$ is equal to
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → -625
Given: $|A| = -5$, and $A$ is a $3 \times 3$ matrix
We use the property: $|\lambda A| = \lambda^n |A|$ for an $n \times n$ matrix
Here, $\lambda = 5$, $n = 3$
So, $|5A| = 5^3 \cdot |A| = 125 \cdot (-5) = {-625}$