Another way of solving this question ....
Lets assume option A) is the answer ...
(i.e) If the given matrix has non-trivial solution,then A) should be TRUE
Taking contra-positive
If A) is FALSE,then the given matrix shouldnot have non trivial solution ...
Let me take p=1,q=1,r=1 (NOTE : Here both conditions in Option A) are false) ... Now determinant value of the given matrix = 0 which means this matrix has non-trivial solution ... So our assumption that "if given matrix has non-trivial solution,then A) should be TRUE" is FALSE ...
The above example not only eliminates A) but also B) and D)
So C) should be the answer ...