Is this set closed under multiplication A={0,1} explain why or why not. Please help ASAP!!!

if you multiply any two elements of A, is the result also an element of A?

If so, then A is closed under multiplication.

To determine whether the set A={0, 1} is closed under multiplication, we need to check if the product of any two elements in the set also belongs to the set.

In this case, the set A={0, 1} contains the two elements 0 and 1.

To check closure under multiplication, we need to multiply each element in the set with every other element and see if the result is in the set as well.

1. Multiplying 0 and 0: 0 * 0 = 0. The result, 0, is in the set A.

2. Multiplying 0 and 1: 0 * 1 = 0. The result, 0, is in the set A.

3. Multiplying 1 and 0: 1 * 0 = 0. The result, 0, is in the set A.

4. Multiplying 1 and 1: 1 * 1 = 1. The result, 1, is in the set A.

As we can see, every possible product of two elements in the set A is also present in the set A. Therefore, set A={0, 1} is closed under multiplication.

Thus, the set A is closed under multiplication because the product of any two elements in the set A is also an element of the set A.