I am not sure where to begin with this question but any guidance will be greatly appreciated:

Question: Let A be a nonsingular matrix and let lambda be an eigenvalue of A. Show that 1/lambda is an eigenvalue of A^-1

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- February 9th 2011, 02:35 PMsparkyShow 1/lambda = eigenvalue of A^-1
I am not sure where to begin with this question but any guidance will be greatly appreciated:

Question: Let A be a nonsingular matrix and let lambda be an eigenvalue of A. Show that 1/lambda is an eigenvalue of A^-1 - February 9th 2011, 03:25 PMFernandoRevilla
If is nonsingular and is an eigenvalue of then, (why?) and there exists column vector such that . Now, multiply both sides by .

Fernando Revilla