Why outer product taken??

Q6. (A) In a system consisting of two spin particles labeled 1 and 2, let S=G and s= denote the corresponding spin operators. Here d=lo,.0,,o.) and Oxy are the three Pauli matrices. In the standard basis the matrices for the operators Ss and s's are respectively, ) o 6 ) (0 10 0 (c)00i 0h|0 0 -i 0 0- O 0 0 0) (0-i 0 0 d 00 0h|i 0 0 0 4 0 00-il 4 |0 0 0 1 o 0i 0 o o1o Ans: (c) Head office fiziks, H.No. 40-D, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IT Hauz Khas, New Delhi-16 Website: www.physicsbyfiziks.com Email: fiziks.physics@gmail.com fiziks fizi Institute for NET/JRF, GATE, IT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES Solution: S's- -1 0 0 0 0 - 0 spis- 0 (B) These two operators satisfy the relation (a)ss,ss}=s'sa) (ssss]-1s'se () Ss.ss-0 Ans: (d) Solution: We have matrix Ss and Ss from question 6(A) so commutation is given by sPs s9se]-o.