Question

If \[ A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & -2 \end{bmatrix}, \] then \( |A| \) is:

• A. 0
• B. -10
• C. 10
• D. 1

Hint:

For a diagonal matrix, the determinant is simply the product of the diagonal elements.

Answer 1

The Correct Option is C

The determinant of a diagonal matrix equals the product of its diagonal entries. For matrix \( A \), with diagonal entries 1, 5, and -2, the determinant is calculated as: \[ |A| = 1 \times 5 \times (-2) = -10. \] Therefore, \( |A| \) is -10.