The Hungarian method needs a square matrix. Extra columns mean too few rows, so a dummy row of zero costs is inserted — hence the statement (which says a dummy column) is False.

The assignment problem assigns each row (say, a worker) to exactly one column (say, a job), so it requires an equal number of rows and columns, i.e. a square $n \times n$ cost matrix.

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A maximization assignment is converted to minimization by subtracting each element from the largest element (forming a loss/regret matrix) — not the smallest — so the statement is False.

The Hungarian method minimizes total cost. To solve a maximization assignment problem (e.g. maximizing profit), it is first converted into an equivalent minimization problem by creating a loss matrix: subtract every element of the profit matrix from the largest element of that matrix.

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