Question

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

(A) 5

(B) 6

(C) at least 7

(D) less than 4

Answer 1

Answer is (C) at least 7

Let us consider the following matrix:

 

which are six non-singular matrices because six blanks (i.e. X) can be filled by five zeros and one 1. In the same manner, we have the matrix

which are six non-singular matrices. Therefore, in the required case, there are more than 7.