If A is decidable, is A* decidable?

Question

my thought process is that since you can construct a Turing machine that decides the language, all you would need to do is construct it so that it continues to accept every time the same valid strings are inputted, but i'm not sure if that's right/how to provide a proper explanation for it.

pseudocode of my understanding:

function PartitionA(s: string, A: set of strings) -> boolean:
n = length(s)

partition = array of size n, initialized to false

# Base case: empty string can always be partitioned into strings in A
partition[0] = true

for i from 1 to n:
    for j from 0 to i:
        # Check if the substring s[j:i] belongs to set A
        if partition[j] is true and A.contains(s[j:i]):
            partition[i] = true
            break

#  last element of array shows if entire string can be partitioned
return partition[n - 1]