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 a matrix \( A \) is given by: \[ \text{det}(A) = ad - bc. \] For \( A = \begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix} \), \[ \text{det}(A) = 2 \times 5 - 3 \times 4 = 10 - 12 = -2. \] Now, the determinant of \( A^2 \) is: \[ \text{det}(A^2) = (\text{det}(A))^2 = (-2)^2 = 4. \] The correct answer is: \[ \boxed{4}. \]