Let A be an invertible matrix and λ be an eigenvalue of A. Prove, using the definition of an eigenvalue, that is 1/ λ an

Question

Let A be an invertible matrix and  λ be an eigenvalue of A. Prove, using the definition of
an eigenvalue, that is 1/ λ an eigenvalue of A-¹.
 If A is an invertible matrix that is diagonalisable, prove that A-¹ is diagonalisable.

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