If A is a `3xx3` matrix such that `|A|=8`, then `|3A|` equals

Options

A. 8
B. 24
C. 72
D. 216

Answer

To solve the problem, we need to find the determinant of the matrix \(3A\) given that the determinant of matrix \(A\) is \(8\) and \(A\) is a \(3 \times 3\) matrix.

### Step-by-Step Solution:

1. **Understand the property of determinants**:
The determinant of a scalar multiple of a matrix can be expressed using the formula:
\[ |kA| = k^n |A| \]
where \(k\) is a scalar, \(A\) is a matrix, and \(n\) is the order of the matrix.

2. **Identify the values**:
Here, we have:
- \(k = 3\) (the scalar multiplier)
- \(n = 3\) (since \(A\) is a \(3 \times 3\) matrix)
- \(|A| = 8\) (the determinant of matrix \(A\))

3. **Apply the formula**:
Using the formula from step 1, we can calculate \(|3A|\):
\[ |3A| = 3^3 |A| \]

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

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

6. **Perform the multiplication**:
\[ 27 \times 8 = 216 \]

7. **Final result**:
Therefore, the determinant of \(3A\) is:
\[ |3A| = 216 \]

### Conclusion:
The value of \(|3A|\) is \(216\).