Basic multiplication table/Last digit/Vector space dimension/Exercise

We consider the last digit in the basis multiplication table as a family of ${}9$-tuples of length ${}9$, that is, the row vectors in the matrix

${\begin{pmatrix}1&2&3&4&5&6&7&8&9\\2&4&6&8&0&2&4&6&8\\3&6&9&2&5&8&1&4&7\\4&8&2&6&0&4&8&2&6\\5&0&5&0&5&0&5&0&5\\6&2&8&4&0&6&2&8&4\\7&4&1&8&5&2&9&6&3\\8&6&4&2&0&8&6&4&2\\9&8&7&6&5&4&3&2&1\end{pmatrix}}.$

What is the dimension of the linear subspace in ${}\mathbb {R} ^{9}$ generated by these tuples?

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