For reflexive relation, ∀(A,A)∈R for matrix P. ⇒‌‌A=PAP−1 is true for P=1 So, R is reflexive relation. For symmetric relation, Let (A,B)∈R for matrix P. ⇒‌‌A=PBP−1 After pre-multiply by P−1 and post-multiply by Pt we get P−1AP=B So, (B,A)∈R for matrix P−1. So, R is a symmetric relation. For transitive relation, Let ARB and BRC So, ‌‌A=PBP−1 and B=PCP−1 Now, ‌‌A=P(PCP−1)P−1 ⇒‌‌A=(P)2C(P−1)2⇒A=(P)2⋅C⋅(P2)−1 ∴(A,C)∈R for matrix P2. ∴R is transitive relation. Hence, R is an equivalence relation.