If A is a square matrix of order 3 and $|A| = 4$, then the value of $|2A^T|$ is

32

The correct answer is Option (4) → 32

Determinant Calculation

$A\text{ is a }3\times 3\text{ matrix with }|A|=4.$

Property: for an $n\times n$ matrix $A$ and scalar $k$, $|kA|=k^{n}|A|$.

Property: $|A^{T}|=|A|$.

Here $n=3$ and $k=2$,

$|2A^{T}|=2^{3}|A^{T}|=8|A|=8\times 4=32$