If A is 2 × 2 and has an eigenvalue c of multiplicity two, then the characteristic polynom...

If A is 2 × 2 and has an eigenvalue c of multiplicity two, then the characteristic polynomial is pA(λ) = (λ − c)2. Because pA(A) = 0 (see the Cayley-Hamilton theorem), (A − cI)2 = 0. Each of the 2 × 2 matrices in Exercises has an eigenvalue c of multiplicity two. Find that eigenvalue c and verify that (A − cI)2 = 0.