1) The set must be non-empty. Most often it is best to show that the 0 vector is in the set. Is it true that 0B= B0?
2) The set must be closed under addition. If AB= BA and CB= BC, that is, if A and B are in the set, is (A+ C)B= B(A+ C)?
3) The set must be closed under scalar multiplication. If AB= BA, that is, if A is in the set, and p is any scalar, is (pA)B= B(pA)?
A counter-example will show that a general statement is NOT true, which is why your first examples were correct. But an example cannot prove that a statement is true.IV) and the same for this one.
I look forward to hearing from you and really appreciate you reading this.