Consider the group homomorphism. f: M2(R) to R given by f(A)= trace(A). Then the kernel of f is isomorphic to which group?Any idea? Plz help me thanks in advance!!!
Do you understand what you are told here? M2(R) is the set of 2 by 2 invertible matrices. The matrix $\displaystyle \begin{pmatrix}a & b \\ c & d \end{pmatrix}$, 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 $\displaystyle \begin{pmatrix}a & b \\ c & -a \end{pmatrix}$ for which -bc- a^2 is not 0.