  In this paper we give an example of a linear group such that its tensor
square is not linear. Also, we formulate some sufficient conditions for the
linearity of non-abelian tensor products $G \otimes H$ and tensor squares $G
\otimes G$. Using these results we prove that tensor squares of some groups
with one relation and some knot groups are linear. We prove that the Peiffer
square of finitely generated linear groups is linear. At the end we construct
faithful linear representations for the non-abelian tensor square of free group
and free nilpotent group.
