Answer to Question #45471 in Abstract Algebra for jasvinder

Question

The map f : R[x] -> M(subscript3)(R) is defined by
f ( a(subscript 0) + a(subscript 1)x + a(subscript 2)x(power 2) + ....... + a(subscript n)x(power n)
_ _
| a(subscript 0) a(subscript 1) a(subscript 2) |
= | 0 a(subscript 0) a (subscript 1) |
|_ 0 0 a(subscript 0) _|
Show that f is a group homomorphism.Determine ker(f) also.