We need to remember an important formula:
det(AB)= det(A)*det(B).
We are given that PQ=PR
Taking determinant both sides and rearranging we have
detP*(detQ-detR)=0
And hence detP=0
Note that detP definitely has to be zero but detQ-detR need not always be zero. Lets assume detP is not zero. That means it's inverse exists.
So P-1(PQ)= P-1(PR)
Q=R which is prohibited in the question.
Hence correct option is only C