Let the sets of eigenvalues and eigenvectors of a matrix 𝐵 be {𝜆_𝑘 |1 ≤ 𝑘 ≤ 𝑛} and {𝒗_𝑘 |1 ≤ 𝑘 ≤ 𝑛}, respectively. For any invertible matrix 𝑃, the sets of eigenvalues and eigenvectors of the matrix 𝐴, where 𝐵 = 𝑃⁻¹𝐴𝑃, respectively, are

{𝜆_𝑘 det(𝐴) |1 ≤ 𝑘 ≤ 𝑛} and {𝑃𝒗_𝑘 |1 ≤ 𝑘 ≤ 𝑛}

{𝜆_𝑘 |1 ≤ 𝑘 ≤ 𝑛} and {𝒗_𝑘 |1 ≤ 𝑘 ≤ 𝑛}

{𝜆_𝑘 |1 ≤ 𝑘 ≤ 𝑛} and {𝑃𝒗𝑘 |1 ≤ 𝑘 ≤ 𝑛}

{𝜆_𝑘 |1 ≤ 𝑘 ≤ 𝑛} and {𝑃⁻¹𝒗_𝑘 | 1 ≤ 𝑘 ≤ 𝑛}

Question Not Attempted

Let the sets of eigenvalues and eigenvectors of a matrix 𝐵 be {𝜆𝑘 |1 ≤ 𝑘 ≤ 𝑛} and {𝒗𝑘 |1 ≤ 𝑘 ≤ 𝑛}, respectively. For any invertible matrix 𝑃, the sets of eigenvalues and eigenvectors of the matrix 𝐴, where 𝐵 = 𝑃−1𝐴𝑃, respectively, are