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Posted: **Tue Sep 07, 2021 7:51 am**

: 19 Show That M2 F Is A Field If And Only If The Equation X2 Y2 0 Does Not Have A Solution In F Other Than 0 0 C 1 (18.9 KiB) Viewed 279 times

: 19 Show That M2 F Is A Field If And Only If The Equation X2 Y2 0 Does Not Have A Solution In F Other Than 0 0 C 2 (18.9 KiB) Viewed 279 times

19 Show that M2(F) is a field if and only if the equation x2 + y2 = 0 does not have a solution in F, other than (0,0). Conclude that G2(F) is a field if F R, Q, or the ternary field. But not if F C, and in the binary field. For a challenge, characterize finite fields for which G2(F) is a field.