Let P1=I=100010001,P2=100001010,P3=010100001P4=010001100,P5=001100010,P6=001010100 and X=∑k=16Pk213102321PkTWhere PkT denotes the transpose of the matrix Pk. Then which of the following options is/ are correct?

Let A=213102321⇒X=∑k=16PkAPkT, Here PkPkT=PkTPk=I for all k=1,2,3,4,5,6 . PkT=Pk-1&AT=A and    XT=∑k=16PkAPkTT=∑k=16PkAPkT=X Let B=111⇒XB=∑K=16PKAPKTB=∑K=16PKAB=∑K=16PKAB=222222222AB=303030=30111=30B∴α=30 and (X-30I) is singular,   Tr∑k=16PkAPkT=18