## Elementary Linear Algebra 7th Edition

The set of all $3\times3$ matrices of the form $$\left[\begin{array}{lll}{0} & {a} & {b} \\ {c} & {0} & {d} \\ {e} & {f} & {0}\end{array}\right]$$ with the standard operations is a vector space. One can see easilly that the set closed under addition and scalar multiplication and all other axioms of the vector space.