could someone elaborate on the following:
A matrix representation of a group $G$ is a homomorphism $R:G\rightarrow GL_n$.
If a group $G$ is given by
$$\langle x_1,\dots,x_n\mid r_1,\dots,r_k\rangle$$
generators and relations and we have matrices $R_{x_1},\dots ,R_{x_n}$ that satisfy the relations, Then we may obtain a matrix representation $R:G\rightarrow GL_n$.
May someone elaborate on why the map is a homomorphism please?