Maximum likelihood covariance estimation of Gaussian

I was reading these notes on matrix calculus

and I could not figure out how to go from equation (30) to (31). Any kind of help is appreciated.

Edit: The oI notation is defined in equation (21).

OK, it's more trivial than I thought: (30) is in the form of A = (A o I)/2, which is satisfied only if A=0, which is a simplified form of (30). Working with A=0, then (31) follows.