If $\mathrm{f}: \mathrm{S} \rightarrow \mathbb{R}$ where $S$ is the set of all non-singular matrices of order 2 over $\mathbb{R}$ and $f\left[\left(\begin{array}{ll}a & b \\ c & d\end{array}\right)\right]=a d-b c$, then

• A

  $\mathrm{f}$ is bijective mapping
• B

  $\mathrm{f}$ is one-one but not onto
• C

  $\mathrm{f}$ is onto but not one-one
• Correct answer
  D

  $\mathrm{f}$ is neither one-one nor onto

Hence, the correct answer is option: 'D'.