The eigenvalues are $\lambda_1 = 1$ and $\lambda_2 = -1$ with eigenvectors $\begin{bmatrix} 1 \\ 0 \end{bmatrix}$ and $\begin{bmatrix} 0 \\ 1 \end{bmatrix}$

F is diagonalizable over $\mathbb{R}$

The eigenvectors are orthogonal

$\det(F) = \lambda_1 \cdot \lambda_2$