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edited Sep 25, 2017 at 17:12

Probably less efficient than Mathe172's answer, but with simpler logic:

Select[Tuples[{1, -1}, {4, 4}], Det[#] =!= 0 && #[[1]] == {1, 1, 1, 1} &]

Select[Tuples[{1, -1}, {4, 4}], Det[#] =!= 0 && #[[1]] == {1, 1, 1, 1} &]

This generates all 4x4 matrices with +/-1 entries, then selects all those with Det not zero and with the specified first row.

Probably less efficient than Mathe172's answer, but with simpler logic:

Select[Tuples[{1, -1}, {4, 4}], Det[#] =!= 0 && #[[1]] == {1, 1, 1, 1} &]

This generates all 4x4 matrices with +/-1 entries, then selects all those with Det not zero and with the specified first row.

Probably less efficient than Mathe172's answer, but with simpler logic:

Select[Tuples[{1, -1}, {4, 4}], Det[#] =!= 0 && #[[1]] == {1, 1, 1, 1} &]

This generates all 4x4 matrices with +/-1 entries, then selects all those with Det not zero and with the specified first row.

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created Sep 25, 2017 at 16:51

Probably less efficient than Mathe172's answer, but with simpler logic:

Select[Tuples[{1, -1}, {4, 4}], Det[#] =!= 0 && #[[1]] == {1, 1, 1, 1} &]

This generates all 4x4 matrices with +/-1 entries, then selects all those with Det not zero and with the specified first row.