If A is a square matrix of order 3 and $∣A∣=5$, then the value of $∣2A|$ is

The correct answer is 40

Given $n=3$ and $|A|=5$

We know that $|kA| = k^n|A|$

In this case, $k$ = 2

⇒ $|2A| = 2^3|A| = 8|A|$



As a square matrix is symmetric, it is equal to its transpose.
⇒ $|A| = |A^T| = |A'|$
∴ $|2A'| = 2^3|A'| = 8|A'| = 8 \times 5 = 40$