Adjacency-matrix quadratic relation for a complete graph

For the adjacency matrix

A

of

K_{n}

,

A = J - I, A^{2} = (n - 2) A + (n - 1) I .

Hence

I, A, A^{2}

are linearly dependent for every

n \geq 2

.

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Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 2 / 17H / d / Solution

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