Exercise 3.1 Discussion

$\def\abs#1{|#1}\def\i{\mathbf {i}}\def\ket#1{|{#1}\rangle}\def\bra#1{\langle{#1}|}\def\braket#1#2{\langle{#1}|{#2}\rangle}\mathbf{Exercise\ 3.1}$
Let $V$ be a vector space with basis $\{(1,0,0), (0,1,0), (0,0,1) \}$. Give two different bases for $V\otimes V$.