1. The problem statement, all variables and given/known data Show that <U,V> = u1.v1 + u2.v3 + u2.v3 + u4.v4 is NOT an inner product on M2x2 2. Relevant equations U: row 1 = [u1 u2] row 2 = [u3 u4] V: row 1 = [v1 v2] row 2 = [v3 v4] 3. The attempt at a solution As I went through each of the axioms, I found that they were all correct (at least the way I did it), I've been stuck for quite some time now. I found that the symmetry axiom, additivity axiom and homogeneity axiom all remained true. So I'm assuming the positivity axiom doesn't hold true, I'm just confused as how to show this.