# Thread: Linear Algebra help - Question 3!

1. ## Linear Algebra help - Question 3!

Determine which of the four inner product axioms do not hold. give a specific example in the case.

In M22, define <A, B> = det(AB)

Let u and v be in R^2.
define <u, v> = u1v1 - u2v2

axioms:
1) <u, v> = <v,u>
2) <u, v+w> = <u, v> + <u, w>
3) <cu, v> = c<u, v>
4) <u, u> greater than or equal to 0 if and only if u = 0

2. Not sure if I am reading this properly or not, but you are working in 2 by 2 matrices with real entries? I will give an example with entries in $\mathbb{Z}$ just to be sure. consider the 2 by 2 matrix with entries all 1. Then A^2 has entries all 2. But the determinant of this matrix is 0, while it is certainly not the 0 matrix.