Step 1: Recall the formula for the determinant of a 2x2 matrix The determinant of a 2x2 matrix \( \begin{vmatrix} a & b \\ c & d \end{vmatrix} \) is calculated as: \[ \text{determinant} = ad - bc \] Step 2: Apply the formula to the given matrix For the matrix \( \begin{vmatrix} 2 & 3 \\ 4 & 5 \end{vmatrix} \), the elements are: - \( a = 2 \), - \( b = 3 \), - \( c = 4 \), - \( d = 5 \). Substitute these values into the determinant formula: \[ \text{determinant} = (2)(5) - (3)(4) = 10 - 12 = -2 \] Answer: The determinant's value is \( -2 \). The correct answer is option (4).