Hello student,

1. R is reflexive

Now, ab != 0

So, a!=0 or b!=0 (neither a nor b can be zero)

Thus, aRa => a.a != 0 => a is not necessarily 0.

So, R is reflexive.

2. R is symmetric

We know that, ab=ba (communicative property of multiplication)

=> aRb = ab != 0 = ba = bRa

So, R is symmetric.

3. R is transitive

Let aRb and bRc be arbitrary such that ab != 0 and bc != 0.                            (...A)

So, in this case b != 0.

Similarly, neither can a = 0 nor c = 0.                                                                  (from A)

Therefore, aRc != 0

So, aRc is true.

Thus, R is transitive.

Hence, R is an equivalence relation also.

I hope it helps!