Answer to Question #44736 in Abstract Algebra for jasvinder

Question #44736

The map φ : R[x] → M(subscript3)(R) is deﬁned by
| a0 a1 a2 |
φ(a0 +a1x+a2x2 +···+anxn) = matrix | 0 a0 a1 |
    | 0 0 a0 | .
Show that φ is a group homomorphism. Determine kerφ also.

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