If $M$ is the set of all $2\times 2$ matrices with real entries and $f :M\rightarrow R$ is defined as $f(A)=|A| \:\forall\:A\in M$, then $f$ is

Question

$\begin{array}{1 1}(A) Bijective \\ (B) Neither 1-1 \;nor\; onto\\ (C) Onto \;but\; not 1-1 \\ (D) 1-1 but \;not\; onto \end{array}$