The number of 3 x 3 non-singular matrices, with four entries as 1 and all other entries as 0 is

The matrix 1    a    bc    1    de    f    1where exactly one of a, b, c, d, e, f is 1 and rest of them are zeros, is invertible.There are six such matrices.Also, the matrix 1    0    10    1    01    0    0 is invertible.Thus, there are at least 7 such matrices which are invertible.