So trying to study chapters on ring homomophisms and integral domains, and there is this one problem in the book where I just don't get how to show the kind of problems yet (as I'm not yet used to it); the problem is:

Show that the matrices $R=\begin{pmatrix}

a & b \\

0 & a \\

\end{pmatrix}$ for $a,b \in \mathbb{R}$ is a subring of the ring of matrices $M_2(\mathbb{R})$, also find a ring homomorphism such that $\Phi:R \rightarrow \mathbb{R}$ that is onto.

I will appreciate the help as I am very new to ring homomoprhisms.

Show that the matrices $R=\begin{pmatrix}

a & b \\

0 & a \\

\end{pmatrix}$ for $a,b \in \mathbb{R}$ is a subring of the ring of matrices $M_2(\mathbb{R})$, also find a ring homomorphism such that $\Phi:R \rightarrow \mathbb{R}$ that is onto.

I will appreciate the help as I am very new to ring homomoprhisms.

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