Show that the following is NOT a (real) vector space: the set of all 2 ×2 matrices, with the usual scalar multiplication, but with addition defined by A ⊕ B = 0, where 0 is the 2 × 2 zero matrix, and...

Show that the following is NOT a (real) vector space: the set of all 2 ×2 matrices, with the usual scalar multiplication, but with addition defined by A ⊕ B = 0, where 0 is the 2 × 2 zero matrix, and ⊕ represents warped addition of 2 × 2 matrices. Justify your answer.