Is there a matrix invariant or property that is multiplicative, $$f(AB)=f(A)f(B),$$ other than the determinant? In addition, some matrix norms are submultiplicative, is there a supmultiplicative property?

Is there a matrix invariant or property that is multiplicative, i.e.,

$$f(AB) = f(A) f(B)$$

other than the determinant? In addition, some matrix norms are submultiplicative, but is there a supermultiplicative property?