1. Is the multiplication of two 2 X 2 matrices commutative?
No. This can be shown be multiplying any two matrices together and then reversing the order. The result will not be the same.
i.e. AB ≠ BA
2. How do I find the additive inverse of a matrix?
All you need to do to find this is change the signs of each element in the matrix. This means then that when you add together the two matrices, the corresponding elements will result in zero. This will give the zero matrix which is the identity matrix for addition.