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Let E be an n×n matrix, and letU= {xE:x∈Rn} (where x∈Rn is written as arow vector)....

Let E be an n×n matrix, and letU= {xE:x∈Rn} (where x∈Rn is written as arow vector). Show that the following are equivalent.
(a) E^2 = E = E^T (T means transpose).
(b) (u − uE) · (vE) = 0 for all u, v ∈ Rn.

(c) projU(v) = vE for all v ∈ Rn.

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