Let A be a `3xx3` determinant and `|A|=7`. Then the value of `|2A|` is.............

Answer

To find the value of \(|2A|\) where \(|A| = 7\) and \(A\) is a \(3 \times 3\) determinant, we can use the property of determinants related to scalar multiplication.

### Step-by-step Solution:

1. **Understand the property of determinants**: For any scalar \(k\) and an \(n \times n\) matrix \(A\), the determinant of \(kA\) is given by:
\[ |kA| = k^n |A| \]
where \(n\) is the order of the matrix.

2. **Identify the values**: In this case, \(k = 2\) (since we are calculating \(|2A|\)), and the order \(n = 3\) (since \(A\) is a \(3 \times 3\) matrix).

3. **Apply the property**: Substitute the values into the property:
\[ |2A| = 2^3 |A| \]

4. **Calculate \(2^3\)**:
\[ 2^3 = 8 \]

5. **Substitute the value of \(|A|\)**: We know that \(|A| = 7\), so:
\[ |2A| = 8 \times 7 \]

6. **Perform the multiplication**:
\[ |2A| = 56 \]

Thus, the value of \(|2A|\) is **56**.