The probability of drawing two aces from a standard deck is 0.0059. we know this probability, but we don't know if the first card was replaced. if the two draws are defined as event a and event b, are the events dependent or independent?

To answer the question we need to know if we replaced or not. 

Lets calculate the 2 probabilities. 

1, No replacement
first draw is an ace P=4/52
2nd draw is an ace P=3/51
Both are A: P=4/52 * 3/51 = 0,0045

2, With replacement
Both draws P=4/52
Both A: P =(4/52)^2 = 0,0059

So we know that it was with replacement. 
This means theat the two events are independent. (both draws have 4/52 chance, not affecting eachother)