1. The problem statement, all variables and given/known data Suppose A and B are vectors. Show that the object Q with nine components Qij=AiBj is a tensor of rank 2. 2. Relevant equations A tensor transforms under rotations (R) as a vector: Tij'=RinRjmTnm 3. The attempt at a solution I wanted to just create the matrix, but I don't know how to prove that this is also a tensor.