Given that A = {0,1, 2,3,... 8, 9}

We need to find the number of symmetric matrices.

We know that a matrix is symmetric if .

Now a 11 , a 22 ,a 33 can have any digit from 0 to 9.

Number of ways this can be done is 10 x 10 x 10 = 10 3 Now a 12 = a 21 . So number of ways this can be done is 10 x 1.

Similarly a 13 = a 31 , So number of ways this can be done is 10 x 1.

Also, a 23 = a 32 . So number of ways this can be done is 10 x 1.

Total symmetric matrix= 10

3 x10x10x10=10 6 Hence this is the correct option.

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