In linear regression we can use A:B to show the first order interaction of variable A and B. But it is hard to know what effect was caused by A and what was caused by B. So I want to understand how exactly A:B worked
it is hard to know what effect was caused by A and what was caused by B
Actually it is not hard, but impossible. First, interaction term in regression tells you on effect of A and B together, rather then about their individual effects. Second, regression per se does not tell you anything about causality.