Identity with scalar product In one proof of some theorem regarding normal distribution there is used I think an idenitity which states $$ (ABy,By)=(B^{-1}ABy,y)$$ where A is symetric and positive, B is orthogonal and y is a vector. Can someone explain to me why is it so?

I assume $(\cdot, \cdot) $ denotes the scalar product. An orthogonal matrix $B$ preserves the scalar product by definition, i.e. $$(Bx,By)=(x,y).$$ Since $B^{-1}$ is also orthogonal, then $$(ABy, By) = (B^{-1}ABy,B^{-1}By)=(B^{-1}ABy,y).$$