Find the zero-one matrix of the transitive closure of the relation with matrix A = [1 0 1; 0 1 0; 1 1 0].

1. A[1 1 1; 0 1 0; 1 1 1]
2. B[1 0 1; 0 1 0; 1 1 0]
3. C[1 0 1; 0 1 0; 1 0 1]
4. D[1 1 1; 0 1 0; 1 0 1]

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Show answer & explanation

Correct answer: A. [1 1 1; 0 1 0; 1 1 1]

Explanation

1 → 3 → 2 gives (1, 2); 3 → 1 → 3 gives (3, 3). Row 1 becomes 111, row 2 stays 010, row 3 becomes 111.