Let A = a i j 3 × 3 be a scalar matrix whose elements are the roots of the equation x 9 - 15 x 8 + 75 x 7 - 125 x 6 = 0 . If A · a d j A = k , then the value of k is equal to

Step-by-step solution

x 9 - 15 x 8 + 75 x 7 - 125 x 6 = 0 ⇒ x 6 ( x - 5 ) 3 = 0 ⇒ x = 0,0 , 0,0 , 0,0 , 5,5 , 5 So, A = 5 0 0 0 5 0 0 0 5 and A = 5 3 A · a d j A = A I = A 3 = 5 3 3 = 5 9