$\text{tr}(AB) = \text{tr}(BA)$ for any conformable $A$ and $B$

$\text{tr}(A) = \text{tr}(A^T)$ for any square matrix $A$

$\text{tr}(M^{-1}) = \frac{1}{\text{tr}(M)}$ for invertible $M$

$\text{tr}(cA) = c \cdot \text{tr}(A)$ for scalar $c$ and square $A$