## Question

###### 3 Show that two square matrices A and B of order n are similar if and only if their eigenvalues coincide and for each eigenvalue A and each i < n have rank(A AE)i = rank(B AE)' .

3 Show that two square matrices A and B of order n are similar if and only if their eigenvalues coincide and for each eigenvalue A and each i < n have rank(A AE)i = rank(B AE)' .

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