The number of symmetric matrices of order 3, with all the entries from the set $$\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}$$ is

A symmetric matrix of order 3 satisfies $$A = A^T$$, meaning $$a_{ij} = a_{ji}$$.

For a 3×3 symmetric matrix, the independent entries are:

• 3 diagonal entries: $$a_{11}, a_{22}, a_{33}$$
• 3 upper triangular entries: $$a_{12}, a_{13}, a_{23}$$

Total independent entries = 6.

Each entry can take any value from the set $$\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}$$, which has 10 elements.

Number of symmetric matrices = $$10^6$$.

This matches option 2: $$10^6$$.