Let a , b and c are the roots of the equation x 3 - 7 x 2 + 9 x - 13 = 0 and A and B are two matrices given by A = a b c b c a c a b and B = b c - a 2 c a - b 2 a b - c 2 c a - b 2 a b - c 2 b c - a 2 a b - c 2 b c - a 2 c a - b 2 , then the value of A B is equal to

Step-by-step solution

a + b + c = 7 a b + b c + c a = 9 a b c = 13 B is the cofactor matrix of A ⇒ B = A 2 ⇒ A ⋅ B = A 3 … . i A = a b c b c a c a b = a b c - a 2 - b b 2 - a c + c a b - c 2 = 3 a b c - a 3 - b 3 - c 3 = - a + b + c a + b + c 2 - 3 a b + b c + c a = - 7 49 - 27 = - 154 From i B A = A 3 = - 154 3