If A is ` 3 xx 3 ` matrix such that |A| = 8, then |3A| equal is

Options

A. 8
B. 24
C. 64
D. 216

Answer

To find the determinant of the matrix \(3A\) when the determinant of matrix \(A\) is given as \( |A| = 8 \), we can follow these steps:

### Step-by-Step Solution

1. **Understanding the Determinant of a Scalar Multiple of a Matrix**:
The determinant of a scalar multiple of a matrix can be expressed as:
\[ |kA| = k^n |A| \]
where \(k\) is a scalar, \(A\) is an \(n \times n\) matrix, and \(n\) is the order of the matrix.

2. **Identify the Given Values**:
Here, \(k = 3\) and \(n = 3\) (since \(A\) is a \(3 \times 3\) matrix). The determinant of matrix \(A\) is given as \( |A| = 8 \).

3. **Applying the Formula**:
Using the formula for the determinant of a scalar multiple:
\[ |3A| = 3^3 |A| \]

4. **Calculating \(3^3\)**:
Calculate \(3^3\):
\[ 3^3 = 27 \]

5. **Substituting the Value of \(|A|\)**:
Now substitute \(|A| = 8\) into the equation:
\[ |3A| = 27 \times 8 \]

6. **Final Calculation**:
Calculate \(27 \times 8\):
\[ 27 \times 8 = 216 \]

### Conclusion
Thus, the determinant of the matrix \(3A\) is:
\[ |3A| = 216 \]