Let A = a i j 3 × 3 and B = b i j 3 × 3 , where b i j = a i j + a j i 2 ∀ i , j . Number of such matrices A whose elements are selected from the set 0 , 1,2 , 3 such that A = B , are

Step-by-step solution

A = a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 and B = b 11 b 12 b 13 b 21 b 22 b 23 b 31 b 32 b 33 ∵ A = B ⇒ a i j = b i j = a i j + a j i 2 ⇒ a i j = a j i ⇒ A is a symmetric matrix Hence, the number of such matrix = 4 × 4 × 4 × 4 × 4 × 4 = 4 6 = 2 12