If is a cube root of unity and is the set of all non-singular matrices of the form if
where each of is either . Then the number of distinct matrices in the set is
As the given set is a set of all the non-singular matrices then the determinant of the given matrix cannot be equal to zero,
Now, solve the determinant to determine the required,
From this, we can conclude that,
Therefore, belongs to
Hence, there can be two distinct matrices.