Question

If A is a square matrix of order 3 such that the determinant $|A| = 5$, what is the value of the determinant $|2A|$?

• A. 10
• B. 25
• C. 40
• D. 8

Hint:

If a matrix of order $n$ is multiplied by a scalar $k$, its determinant becomes $k^n$ times the original determinant.

Answer 1

The Correct Option is C

Step 1: Recall the determinant property.
For any square matrix $A$ of order $n$, if each element of the matrix is multiplied by a constant $k$, then the determinant is multiplied by $k^n$.
Step 2: Apply the formula.
Here, the order of matrix $A$ is $3$, and the scalar multiplier is $2$. Hence, \[ |2A| = 2^3 |A| \]
Step 3: Substitute the given value.
\[ |2A| = 8 \times 5 = 40 \]
Step 4: Conclusion.
Therefore, the value of the determinant $|2A|$ is $40$.