Mathematics

Mathematics

Problem

Let PP be a square matrix such that P2=I−PP^2 = I - P. For α,β,γ,δ∈N\alpha, \beta, \gamma, \delta \in \mathbb{N}, if Pα+Pβ=γI−29PP^\alpha + P^\beta = \gamma I - 29P and Pα−Pβ=δI−13PP^\alpha - P^\beta = \delta I - 13P, then α+β+γ+δ\alpha + \beta + \gamma + \delta is equal to

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