#44 properties of matrix | if λ eigen value of matrix A show that |A|/λ is eigen value of adj(A)

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11. IF 11. IF 'λ' IS AN EIGEN VALUE OF A NON SINGULAR MATRIX 'A' THEN | A| /λ IS AN EIGEN VALUE OF adjA.
12. IF 12. IF 'λ' IS AN EIGEN VALUE OF AN ORTHOGONAL MATRIX 'A' THEN 1 /λ IS ALSO AN EIGEN VALUE OF A.
10. IF 10. IF 'λ' IS AN EIGEN VALUE OF A NON SINGULAR MATRIX 'A' THEN 1/λ IS AN EIGEN VALUE OF A⁻¹.
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Show that λ is an eigenvalue of A and find a corresponding eigenvector Show that λ is an eigenvalue of A and find a corresponding eigenvector