Question

The number of $3\times 3$ non-singular matrices with four entries as $1$ and all other entries as $0$ is

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

Answer 1

The correct option is B less than $4$

According to the question,

First consider the number of non-singular matrices with $3$ entries $1$ and the rest 0,

They must have one $1$ in each of the row and columns, so the only possibilities are,

For each of these $6$ possibilities we can make any one of the remaining six $0^{\prime }s$ into a

$1.$ These are all distinguishable. So ther ara a total of $6\ast 6=36$ non-singular $3\ast 3$ matrices with 4 entries being $1$ and the emaining $5$ entries $0$