Question

Find the determinant of the matrix \( A = \begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix} \).

• A. 0
• B. 4
• C. 9
• D. 25

Hint:

For a 2x2 matrix \( \begin{bmatrix} a & b
c & d \end{bmatrix} \), use the formula \( \text{det}(A) = ad - bc \) to calculate the determinant.

Answer 1

The Correct Option is A

The determinant of a 2x2 matrix \( A = \begin{bmatrix} a & b \\ c & d \end{bmatrix} \) is given by: \[ \text{det}(A) = ad - bc. \] For the matrix \( A = \begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix} \), we have: \[ \text{det}(A) = 2 \times 5 - 3 \times 4 = 10 - 12 = -2. \] Thus, the determinant of the matrix is: \[ \boxed{-2}. \]