The exception is the non-negative monomial matrices : a non-negative matrix has non-negative inverse if and only if it is a ( non-negative ) monomial matrix.
2.
In more generality, if there is an n \ times n monomial matrix M \ colon \ mathbb { F } _ q ^ n \ to \ mathbb { F } _ q ^ n which sends C 1 isomorphically to C 2 then we say C 1 and C 2 are "'equivalent " '.
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