First of all , an equivalence relation is a relation that is transitive, symmetric as well as reflexive. Also a relation on A means that the relation R is from the set A to the set A itself.
First, the first digit of any number is obviously equal to its own first digit, hence the relation is reflexive.
Secondly, Consider 2 elements whose first digits are same , say a and b. Again, it is clear that the first digit of b and a are also same, hence it is a symmetric relation
Lastly, Suppose 2 elements a and b have the same first digit and so do two elements b and c. Clearly, the first digit of a and c are also equal each being equal to the first digit of b. Hence, R is transitive
Finally since the relation is symmetric, transitive as well as reflexive, the relation R is an equivalence relation