The number of 3 x 3 non-singular matrices, with four entries as 1 and all other entries as 0, is:- (1) 5 (2) 6 (3) at least 7 (4) less than 4

Options

A. 6
B. at least 7
C. less than 4
D. 5

Answer

B

Explanation

Taking each leading diagonal entry as 1 and remaining all entries as zero except one which is equal to 1, we get 6 non-singular matrices as given below:
`[(1,1,0),(0,1,0),(0,0,1)], [(1,0,1),(0,1,0),(0,0,1)], [(1,0,1),(0,1,1),(0,0,1)],[(1,0,0),(1,1,0),(0,0,1)],[(1,0,0),(0,1,0),(0,1,1)],[(1,0,0),(0,1,0),(1,0,1)]`
Similarly, we obtain following non-singular matrices
`[(0,0,1),(0,1,1),(1,0,0)],[(0,0,1),(1,0,1),(1,0,0)]` etc
So, option (b) is correct