Question

Let \( M \) be the set of all \( 2 \times 2 \) matrices with entries from the set \( R \) of real numbers. Then the function \( f : M \to R \) defined by \( f(A) = |A| \) for every \( A \in M \) is

• A. neither one-one nor onto
• B. one-one but not onto
• C. onto but not one-one
• D. one-one and onto

Hint:

Determinant maps matrices to real numbers, but different matrices can have the same determinant, so injectivity usually fails.

Answer 1

The Correct Option is C