Question: A 3 3 matrix B is known to have eigenvalues 0, 1, 2. This information is enough to find three of these (give the answer

A 3 3 matrix B is known to have eigenvalues 0, 1, 2. This information is enough to find three of these (give the answer when possible):

(i) the rank of B

(ii) the determinant of BTB

(iii) the eigenvalues of BTB

(iv) the eigenvalues of (B2 + I)-1

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