A = a 2 15 31 12 b 2 41 35 61 c 2 and B = 2 a 3 5 2 2 b 8 1 4 2 c - 3 are two matrices such that the sum of the principal diagonal elements of both A and B are equal, then the product of the principal diagonal elements of B is

Step-by-step solution

Principal diagonal elements of A and B are a 2 ,   b 2 ,   c 2 and 2 a ,   2 b ,   2 c - 3 . According to given condition, a 2 + b 2 + c 2 = 2 a + 2 b + 2 c - 3 ⇒ a 2 + 1 - 2 a + b 2 + 1 - 2 b + c 2 + 1 - 2 c = 0 ⇒ a - 1 2 + b - 1 2 + c - 1 2 = 0 ∴ a - 1 = 0 ,   b - 1 = 0 ,   c - 1 = 0 ⇒ a = 1 ,   b = 1 ,   c = 1 Now, 2 a 2 b 2 c - 3 Putting the values of a ,   b and c we get, = 2 × 2 × - 1 = - 4