Question

Let $A$ be the set of all $3 \times 3$ symmetric matrices all of whose entries are either 0 or 1 . Five of these entries are 1 and four of them are $0$.The number of matrices in $A$ is

• A. 12
• B. 6
• C. 9
• D. 3

Answer 1

Answer: (A)

If two zero's are the entries in the diagonal, then
${ }^{3} C _{2} \times{ }^{3} C _{1}$
If all the entries in the principle diagonal is 1 , then
${ }^{3} C _{1}$
$\Rightarrow $ Total matrix $=12$