Do you understand what you are told here? M2(R) is the set of 2 by 2 invertible matrices. The matrix $\begin{pmatrix}a & b \\ c & d \end{pmatrix}$, such that ad- bc is not 0, is mapped to a+ d. In particular, the "kernel" of this homomorphism is the set of all matrices $\begin{pmatrix}a & b \\ c & -a \end{pmatrix}$ for which -bc- a^2 is not 0.