Question

If \( A = \begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix} \), find the determinant of \( A^2 \).

• A. 0
• B. 4
• C. 9
• D. 25

Hint:

For the determinant of \( A^2 \), square the determinant of \( A \).

Answer 1

The Correct Option is B

The determinant of matrix \( A \) is calculated as \( \text{det}(A) = ad - bc \). For \( A = \begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix} \), \( \text{det}(A) = 2 \times 5 - 3 \times 4 = 10 - 12 = -2 \). The determinant of \( A^2 \) is \( \text{det}(A^2) = (\text{det}(A))^2 = (-2)^2 = 4 \). The final answer is \( \boxed{4}. \)