Question: Let F be a field. Let C' be a 2 x 2 matrix, C := [On C12 E F2x2 C21 22 (a) Prove that if

Let F be a field. Let C' be a 2 x 2 matrix, C := [On C12 E F2x2 C21 22 (a) Prove that if there exist two 2 x 2 matrices A and B such that C = AB - BA, then Cu + C22 = 0. (b) Assume that C12 = C21 and F is the field with two elements. Show that if Call+ C22 = 0, then there exist two 2x 2 matrices A and B such that C = AB-BA

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