Let Aand Bbe 2 × 2 matrices.
a.Show that the sum of the terms on the main diagonal of AB− BAis 0.
b. If Mis a 2 × 2 matrix and the sum of the main diagonal entries is 0, show there is a constant c such that
M2 = cI
c.If A,B, and Care 2 × 2 matrices, then use parts (a) and (b) to show that
(AB − BA)2C= C(AB− BA)2
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