please show me specific process of this answer Thanks a lot

please show me specific process of this answer

Thanks a lot!

Let n be an integer. (a) Prove that if n^2 is a multiple of 5 then n is a multiple of 5. (b) If n^2 is a multiple of 12 does it follow that n is a multiple of 12? Answer yes or no then justify your answer.

Solution

a)

Prove the contrapositive

If n is not a multiple of 5

Then n does not have 5 as a prime factor

HEnce, n^2 does not have 5 as a prime factor

Hence proved

b)

False

Counterexample

6^2=36 is a multiple of 12

But, 6 is not

This statement turns out to be incorrect because 12 is not prime unlike in part a. where 5 was prime.