WBJEE · Maths · Functions
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
- D \(\mathrm{f}\) is neither one-one nor onto
Answer & Solution
Correct Answer
(D) \(\mathrm{f}\) is neither one-one nor onto
Step-by-step Solution
Detailed explanation
Hint : \(\mathrm{f}\left[\left(\begin{array}{ll}2 & 0 \\ 0 & 2\end{array}\right)\right]=4=\mathrm{f}\left[\left(\begin{array}{ll}4 & 0 \\ 0 & 1\end{array}\right)\right]\) \(\Rightarrow\) not one-one As \(0 \in \mathbb{R}\) but S does not contain any singular matrix so, \(f\) is…
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