Let $\displaystyle B$ be an $\displaystyle n \times n$ invertible matrix. Define $\displaystyle \Phi: M_{n \times n}(F) \ \mbox{by} \ \Phi (A) =B^{-1}AB$ Prove that $\displaystyle \Phi $ is an isomorphism.

From the answer provided, it shows:

Let $\displaystyle A =B^{-1}CB \Rightarrow \Phi A = \Phi B^{-1}CB \Rightarrow {\color{blue} B}(B^{-1}CB){\color{blue} B^{-1}} = C$

where do the values in blue come from?