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1. Define F sub four to be the set of all 2x2 matrices.
F(sub 4)= [ a b ] ; a,b elements of F sub 2b a+b
i) Prove that F sub four is a commutative ring whose operations are matrix addition and matrix multiplication
ii) prove that F sub four is a field having exactly four elements
iii) show that I sub four is not a field
F sub four= finite field having 4 elementsF sub two= finite field having 2 elementsI sub four= integers modulo four
2. Show that if f(x)= (x^p)-x element F sub p[x], then its polynomial function (f^beta): F sub p ---->F sub p is identically zero
(capital F sub p is finite field having p elements.f^beta is function raised to power of beta)
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