Option a) P (Q+R)=PQ+QR is wrong because matrix multiplication is not commutative .
option b) ( P-Q)^2 should be P^2 -PQ-QP +Q^2
WE can't write 2pq here because PQ and QP are not same in matrix multiplication.
Option c) it is not the property of determinant .
Option d has written correctly here.so answer is option d