The number of 3×3 non-singular matrices, with four entries as 1 and all other entries as 0, is
Solutions · 1
Official solution
Placing four 1's (and five 0's) so that the resulting matrix is non-singular: patterns with 1's down the main diagonal plus one extra off-diagonal 1 give 6 non-singular matrices (choosing which off-diagonal position among 6 gets the extra 1, while keeping the determinant non-zero --- but degenerate placements must be excluded, leaving 6 valid ones), and additional arrangements not fixing the full diagonal contribute further valid non-singular matrices --- giving a total count of at least 7.