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Let (V, K) be a vector space and π1, π2 be projections on V . If...

Let (V, K) be a vector space and π1, π2 be projections on V . If π1 and π2 commute, i.e. π1 ◦ π2 = π2 ◦ π1, is it true or false that π = π1 + π2 − π1 ◦ π2 is also a projection?

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