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###### Saima posted an Question
October 02, 2021 • 21:38 pm 20 points
• CSIR NET
• Physical Sciences

## Plz solve this matrix question

Q84 he 2x2 idetity matrix| and the Pauli matrices o,.,,o, do not form a group under matrix multiplication. The minimum number of 2x2 matrices, which includes these four matrices, and form a group (under matrix multiplication) is )20 (b) 8 (c) 12 (d) 16 Ans. (d) ixlixI|, o, io, -id O ixl -IXIO, O, O TO, O.

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• ##### Bidyut sinha

see the first page...where u can see the definition of Group...Now in the second page ,the Matrices that I have written that will follow all properties of group...such as {I, sigma x} Check this ...here first (I *sigma x)=sigma x belongs to that group...so proof of (a) closure property... Similar it follows all the property of the group...Such a way, we can form 16 matrices that I have written...

• ##### Bidyut sinha

please see attached picture.minimum 16 number of 2×2 Matrix is possible...

how...? not getting ur point

ok I am explaining you by writing ... wait little bit

see the first page...where u can see the definition of Group...Now in the second page ,the Matrices that I have written that will follow all properties of group...such as {I, sigma x} Check this ...here first (I *sigma x)=sigma x belongs to that group...so proof of (a) closure property... Similar it follows all the property of the group...Such a way, we can form 16 matrices that I have written...

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