Question: Let E be a 2 2 matrix such that E2 = E. Show that M22 = U W, where U = [A |

Let E be a 2 × 2 matrix such that E2 = E. Show that M22 = U ⊕ W, where U = [A | AE = A} and W = [B | BE = 0}. [Hint: XE lies in U for every matrix X.]

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