Pls explain to me step by step

The Cayley-Hamilton theorem from Linear Algebra states that if A is an n x n matrix
with characteristic polynomial p(λ-det(A-AI) then p(A) 0, where the last 0 is
the n × n zero matrix. Verify that Cayley-Hamilton holds for the matrix
2 -2 0
A 0 2 0
-2 2 2
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Transcribed Image Text

The Cayley-Hamilton theorem from Linear Algebra states that if A is an n x n matrix with characteristic polynomial p(λ-det(A-AI) then p(A) 0, where the last 0 is the n × n zero matrix. Verify that Cayley-Hamilton holds for the matrix 2 -2 0 A 0 2 0 -2 2 2