This is wrong, can you see why?

Open,2. (I - A)(I + A) = I - A^2

Hint: the produce of invertible matrices is invertible.3. A^9 is invertible

4. (A + A^-1)^3 = A^3 + A^-3

Try to find a counterexample.5. AB = BA

Open, [tex]A^2 + B^2 + AB + BA[/mat].6. (A+B)^2 = A^2 + B^2 + 2AB

Therefore, you are assuming that which is not always true.