Let $A = [a_{ij}]_{3×3}$ such that $|A| = −5$. Then the value of $\text{det (5A)}$ is equal to

-625

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, $|5A| = 5^3 \cdot |A| = 125 \cdot (-5) = {-625}$