Mark the correct A. one-one and onto

B. neither one-one nor onto

C. one-one not one-one

D. onto but not one-one

Given that M is the set of all 2 × 2 matrices with entries from the set R of real numbers. Then the function f: M → R defined by f(A) = |A| for every A ϵ M.

If f(a) =f(b)

⇒ |a| = |b|

But this does not mean that a=b.

So, f is not one-one.

As a ≠ b but |a|=|b|

So, f is onto.