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Linear Algebra Problem
Question: A square matrix A is said to be idempotent if A2 = A. Let A be an idempotent matrix.(a) Show that I - A is also idempotent.(b) Show that if A is invertible, then A = I.(c) Show that the only possible eigenvalues of A are 0 and 1. (Hint: Suppose x is an eigenvector with associated eigenvalue λ and then multiply x on the left by A twice.)
If A is idempotent then we have to prove that (I-A)is idempotent:
b) It is given that A is invertible matrix so
c) Using the characteristics equation Ax=λx
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