Getting the value of a matrix for formulation

Question

I have a matrix $Y = G_1\times D \times G_2$ where $G_1$, $D$ and $G_2$ are unitary matrices. My question is to get the matrix $Z$ which makes $G_1\times D \times G_2 = D \times Z$

Answer 1

This is just so simple! $$ Z = D^{-1} G_1 D G_2 = \overline{D}^{\mathrm{T}}G_1DG_2$$ since unitary matrices are invertible. I wonder if there is special background behind it.