I was reading these notes on matrix calculus http://research.microsoft.com/en-us/um/people/minka/papers/matrix/minka-matrix.pdf

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.