Question

The number of matrices of order 3 × 3, whose entries are either 0 or 1 and the sum of all the entries is a prime number, is _________.

Answer 1

In a 3 × 3 order matrix there are 9 entries.
These nine entries are zero or one.
The sum of positive prime entries are 2, 3, 5 or 7.
Total possible matrices
=$\frac{9!}{2!⋅7!}$+$\frac{9!}{3!⋅6!}$+$\frac{9!}{5!⋅4!}$+$\frac{9!}{2!⋅7!}$
= 36 + 84 + 126 + 36
= 282