$f(u,w) = u^tAw$ - $f$ is a linear space
What must be NOT TRUE about $A$?
$A$ is symmetric
$AA^t$ is orthogonal
($A-I$) is symmetric
$tr(A-A^t) = 0$
What i though is the $f$ represent a bilinear form, and its symmetric because it represents an inner product space so $f(u,w) = f(w,u)$ therefore, i can conclude that $A$ is symmetric (i think).
Therefore, i conclude that $(1),(4),(3)$ must be true i think.
Therefore i try to prove that $AA^t$ is not true:
Lets look at $AA^t(AA^t)^t = AA^tA^tA =? I$(checking orhogonality of $A$) and i dont know how to prove that its false, if its realy false.
help?