Question

If $A$ is a square matrix of order 3 and $|A|=5$, then the value of $|2A^{T}|$ is

• A. -10
• B. 10
• C. 40
• D. -40

Hint:

When a constant comes out of a determinant, it is raised to the power of the matrix order.

Answer 1

The Correct Option is C

Step 1: Concept
Use the properties $|kA| = k^n |A|$ (where $n$ is the order) and $|A^T| = |A|$.

Step 2: Meaning
Here, the scalar $k = 2$ and the order $n = 3$. The transpose does not change the determinant value.

Step 3: Analysis
$|2A^T| = 2^3 \cdot |A^T| = 8 \cdot |A|$. Substituting $|A| = 5$: $8 \cdot 5 = 40$.

Step 4: Conclusion
The resulting value is 40.
Final Answer: (C)