# Are the left and right unitor maps of the unit object in a monoidal category the same?

Suppose we have a monoidal category $$\mathbb{C}$$, with monoidal product $$\otimes$$, monoidal unit $$I$$, left unitor components $$I \otimes A \overset{\lambda_A}{\rightarrow} A$$ and right unitor components $$A \otimes I \overset{\rho_A}{\rightarrow} A$$. In this case is it true that $$\lambda_I = \rho_I$$? If so what is the proof?