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What's wrong with

sage:  M=matrix(SR, [[6,-2,-1],[3,1,-1],[2,-1,2]]);M
[ 6 -2 -1]
[ 3  1 -1]
[ 2 -1  2]
sage: V=M.eigenvectors_left();V
[(3, [(1, -1, 0)], 3)]
sage: V[0][1][0]*M
(3, -3, 0)
sage: V=M.eigenvectors_right();V
[(3, [(1, 1, 1)], 3)]
sage: M*(V[0][1][0])
(3, 3, 3)

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