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Decide which of the following are ring homomorphisms from M₂(Z) to Z: \text { (a) }\left(\begin{array}{ll}

a & b \\

c & d

\end{array}\right) \mapsto a \quad \text { (projection onto the } 1,1 \text { entry) } \text { (c) }\left(\begin{array}{ll}

a & b \\

c & d

\end{array}\right) \mapsto a d-b c \text { (the determinant of the matrix). } \left(\begin{array}{ll}

a & b \\

c & d

\end{array}\right) \mapsto a+d \quad \text { (the trace of the matrix) }

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