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Group and ring homomorphisms

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Please attached for the question to help me understand Group and Ring Homomorphisms.

Is this function a Homomorphism?
a) Does 1:22 :22 where 1(a1,a2) = (a1,0) define a group homomorphism? a ring homomorphism? Prove your answers.

b) Does 1:22 :22 where 1(a1,a2) = (a2,,a1) define a group homomorphism? a ring homomorphism? Prove your answers.

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https://brainmass.com/math/ring-theory/group-ring-homomorphisms-240814

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This solution provides examples of defining group and ring homomorphisms.

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