Let $A=\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$  where a, b, c, d are positive integers arranged in ascending order, and exactly two of a, b, c, d are prime numbers and also pair wise coprime and satisfies $A^2–16A –17I = 0$(where $I$ is an Identity matrix of order $2\times 2$ ). If $B=\left[\begin{array}{cc}b& a\\ c& d\end{array}\right]$  , then $DetB$  equals ______

Tr(A) = 16, Det(A) = – 17
a + d = 16 and ad – bc = – 17
Given a < b < c < d  
(a, d) = (1,15) (2,14) (3,13) (4,12) (5,11) (6,10) (7,9)
bc = ad + 17 = 32, 45, 56 , 65 , 72 , 77 , 80
(b, c) = (4, 8) (5, 9) (7, 8) (5, 13) (8, 9) (7, 11) (8, 10)
(a, b, c, d) = (1, 4, 8, 15) (2, 5, 9, 14) (3, 7, 8, 13) (4, 5, 13, 12) 
(5, 8, 9, 11) (6, 7, 11, 10) (7, 8, 10, 9)
Possible values are  (2, 5, 9, 14) (3, 7, 8, 13)  (5, 8, 9, 11) 
Exactly two of a, b, c, d are prime and pair wise also coprime
Case : 1 (2, 5, 9, 14)   2 primes but pair wise not coprime 
Case : 2 (3, 7, 8, 13)   3 primes and pair wise coprime (given exactly two are primes) 
Case : 3 (5, 8, 9, 11)   2 primes and pair wise coprime
Only possible answer is (5, 8, 9, 11)
  = bd – ac = 88 – 45 = 43