Question

A, P, B are \( 3 \times 3 \) matrices. If \( |B| = 5 \), \( | BA^T | = 15 \), \( | P^T AP | = -27 \), then one of the values of \( | P | \) is:

• A. 3
• B. -5
• C. 9
• D. 6

Hint:

When solving determinant equations involving matrix properties, always use: \[ |AB| = |A||B|, \quad |A^T| = |A| \]