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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

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

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Two or more different matrices can have same determinent.
$\therefore $ $f$ is many to one but not 1-1 function.
Each real number can be determinent of any matrix.
$\therefore $ $f$ is onto function.
answered May 12, 2013 by rvidyagovindarajan_1

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