Suppose that a is a nonsingular matrix with an eigenvalue λ. show that 1/λ is then an eigenvalue of a-1 .

PROOF:

Suppose that A is an invertible non singular matrix.

Then,

This shows that if A is non singular invertible matrix ad if  λ is eigenvalue of A then  λ⁻¹ is eigenvalue of A⁻¹.

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step-by-step explanation: