Verify the Cayley-Hamilton Theorem for

That is, find the characteristic polynomial cA(λ) of A and show that cA(A) = 0.
An important theorem in advanced linear algebra says that if cA (λ) is the characteristic polynomial of the matrix A, then cA (A) = 0 (in words, every matrix satisfies its characteristic equation). This is the celebrated Cayley-Hamilton Theorem, named after Arthur Cayley (1821 - 1895), pictured below, and Sir William Rowan Hamilton. Cayley proved this theorem in 1 858. Hamilton discovered it, independently, in his work on quaternions, a generalization of the complex numbers.

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