Show that if A is regular, then the subset containing only even language strings, is also regular A language A, even(A) is the subset of A consisting of those strings in A of even length:

even(A) = { x∈A | |x| is even}


I need to use closure properties show that if A is regular, then even(A) is also regular.

Isn't that a definition called "A language is called a regular language if some finite automaton recognizes it", could prove even(A) is regular? How to use closure properties to prove this question?
Could you make a FA that accepts all and only even-length strings? What do you know about the intersection of two regular languages?