Let A be an n x n - matrix over C. Recall that A is diagonalizable if and only if there* exists an invertible matrix B such that B- 1 AB - D where D...

Solve problem 3 from Advanced Linear Algebra relatef to Matrices and eigen vectors.

3. Let A be an n x n - matrix over C. Recall that A is diagonalizable if and only if there*exists an invertible matrix B such that B- 1 AB - D where D is a diagonal matrix .Show that A is diagonalizable if and only if (" has a basis of eigenvectors of A .