the multiplication map $\mu : SL(2,\mathbb{R})×SL(2,\mathbb{R}) → SL(2,\mathbb{R})$ is $C^{\infty}$

Question

I'm not able to show that the multiplication map $\mu : SL(2,\mathbb{R})×SL(2,\mathbb{R}) → SL(2,\mathbb{R})$ is $C^{\infty}$, where GL are the square matrices of determinant 1, how can I prove?