Question

Q4. If R be the group of real numbers under addition and let R be the group of positive real number under multiplication. Let f: R-R' be defined by fix) = e' then show that fis Homomorphism mapping.​

Answer 1

Answer:

Correct option is D)

f:M→R defined by f(A)=∣A∣ for every A∈M

The function is the determinant of the matrix

We know that, two different matrices can have a same determinant

For example, A=[

1

1

0

1

] and B=[

2

1

1

1

]

Then ∣A∣=1=∣B∣, but A



=B

So, the function will not be one-one.

Now, determinants can have any real values, so range of the function will be R.

Thus, the function will be onto.

Hence, option D is correct