For square matrices A and B of same order which of the following is not true. (with real entries) (O is null matrix and I is Identity matrix of same order as A and B)

If AB = O and A is not null matrix then B is singular matrix

If A is skew symmetric then adjoint of A can be skew symmetric.

If AB = O then ${\left(\det A\right)}^2+{\left(\det B\right)}^2\ne 0$

If AB = I then BA =I