a generalized eigenvalue related inequality $\frac{{{x^T}{A^{ - T}}PAx}}{{{x^T}Px}} \le \frac{1}{{{{\left| A \right|}^2}}}$

Question

Does the following inequality always hold? $\frac{{{x^T}{A^{ - T}}PAx}}{{{x^T}Px}} \le \frac{1}{{{{\left| A \right|}^2}}}$, where A is a invertible matrix and P is a positive-definite matrix, x is a column vertor.