We know that a = ± b and a2 = b2 are equal
It is given that {(a, b): a, b ∈ S and a2 = b2}
Here, (a, a) ∈ R and a2 = a2 is true.
Hence, R is reflexive where (a, b) ∈ R
We know that a2 = b2 and b2 = a2 where (b, a) ∈ R
Hence, R is symmetric.
If (a, b) ∈ R and (b, c) ∈ R
We know that a2 = b2 and b2 = c2 we get a2 = c2 where (a, c) ∈ R
Hence, R is transitive.