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

Step-by-step solution

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 A τ = A . A = a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 Now a 11 , a 22 , a 33 can have any digit from 0 to 9 . Number of ways this can be done is 10 × 10 × 10 = 10 3 Now a 12 = a 21 . So number of ways this can be done is 10 × 1 . Similarly a 13 = a 31 , So number of ways this can be done is 10 × 1 . Also, a 23 = a 32 . So number of ways this can be done i