2.II.10C
(i) Let be an matrix with entries in C. Define the determinant of , the cofactor of each , and the adjugate matrix . Assuming the expansion of the determinant of a matrix in terms of its cofactors, prove that
where is the identity matrix.
(ii) Let
Show the eigenvalues of are , where , and determine the diagonal matrix to which is similar. For each eigenvalue, determine a non-zero eigenvector.
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