If determinant A is order `2xx2` and `|A|=3`, then the value of `|2A|` is

Options

A. `6`
B. `12`
C. `-6`
D. None of these

Answer

To find the value of \(|2A|\) given that \(|A| = 3\) and \(A\) is a \(2 \times 2\) matrix, we can use the property of determinants regarding scalar multiplication.

### Step-by-Step Solution:

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

2. **Identify the values**:
In our case:
- The scalar \(k = 2\)
- The order of the matrix \(n = 2\) (since \(A\) is a \(2 \times 2\) matrix)
- The determinant of \(A\) is given as \(|A| = 3\).

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

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

5. **Substitute \(|A|\)**:
Now substitute \(|A| = 3\):
\[ |2A| = 4 \cdot 3 \]

6. **Perform the multiplication**:
\[ |2A| = 12 \]

### Final Answer:
Thus, the value of \(|2A|\) is \(12\).

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