Find |A| if `A = | (5 , 2) , (6 , 3)|`

Options

A. -7
B. 7
C. -2401
D. 2401

Answer

To find the determinant of the matrix \( A = \begin{pmatrix} 5 & 2 \\ 6 & 3 \end{pmatrix} \), we will use the formula for the determinant of a 2x2 matrix.

### Step-by-Step Solution:

1. **Identify the elements of the matrix**:
\[ A = \begin{pmatrix} a & b \\ c & d \end{pmatrix} = \begin{pmatrix} 5 & 2 \\ 6 & 3 \end{pmatrix} \]
Here, \( a = 5 \), \( b = 2 \), \( c = 6 \), and \( d = 3 \).

2. **Use the determinant formula for a 2x2 matrix**:
The determinant \( |A| \) of a 2x2 matrix is given by:
\[ |A| = ad - bc \]

3. **Substitute the values into the formula**:
\[ |A| = (5)(3) - (6)(2) \]

4. **Calculate the products**:
\[ |A| = 15 - 12 \]

5. **Perform the subtraction**:
\[ |A| = 3 \]

### Final Answer:
\[ |A| = 3 \]