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

The correct option is A $12$

If two zeros 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 $=12.$