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Groups and FieldsHardGroups and the Group Axioms

Groups and the Group Axioms · Hard problem

The table below is supposed to be the addition table of Z6\mathbb Z_6 (∗* entry in row ii, column jj, equal to (i+j) mod 6(i+j)\bmod6), but two entries have been corrupted, each creating a repeated value in its row:

∗012345001234511234502234504334501244201235501234\begin{array}{c|cccccc} * & 0&1&2&3&4&5\\\hline 0&0&1&2&3&4&5\\ 1&1&2&3&4&5&0\\ 2&2&3&4&5&0&4\\ 3&3&4&5&0&1&2\\ 4&4&2&0&1&2&3\\ 5&5&0&1&2&3&4\end{array}

Find the sum of the two repeated values (the one in row 22 plus the one in row 44).