The matrix cookbook:

http://orion.uwaterloo.ca/~hwolkowi/matrixcookbook.pdf

is a free resource will all sorts of useful identities involving various decompositions, forms of inverses for various commonly encountered matrix structures, formulas for differentiating matrix functions and much more. You'll probably find whatever you're looking for in the matrix cookbook. I've never found any mistakes at all there, but since the matrix cookbook is a free resource, it is not professionally edited, so there could potentially be errors there. But, it is regularly being updated, so I wouldn't worry too much about that.

Although this is a general purpose manual, there is certainly a statistics slant to it, as you will see.

The Matrix Cookbook by K. B. Petersen.

is a free resource will all sorts of useful identities involving various decompositions, forms of inverses for various commonly encountered matrix structures, formulas for differentiating matrix functions and much more. You'll probably find whatever you're looking for in the matrix cookbook. I've never found any mistakes at all there, but since the matrix cookbook is a free resource, it is not professionally edited, so there could potentially be errors there. But, it is regularly being updated, so I wouldn't worry too much about that.

Although this is a general purpose manual, there is certainly a statistics slant to it, as you will see.