The final matrix (in decreased row echelon kind) has two non-zero rows and so the rank of matrix A is two.
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A typical method of acquiring the rank of the matrix is to reduce it to a less complicated form, commonly row echelon form, by elementary row functions. Row operations tend not to change the row Room (hence usually do not alter the row rank), and, being invertible, map the column Area to an isomorphic Place (hence do not change the column rank).
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Matrix rank should not be confused with tensor order, which is called tensor rank. Tensor order is the number of indices needed to generate a tensor, and so matrices all have tensor buy two.
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