Question

We say two n × n matrices A and B are similar if there is an...

We say two n × n matrices A and B are similar if there is an invertible n × n matrix P such that

A = PBP^ -1.

a) Show that if A and B are similar n × n matrices, then they must have the same determinant.

b) Show that if A and B are similar n × n matrices, then they must have the same eigenvalues.

c) Give an example to show that A and B can be similar n × n matrices, but have different eigenvectors.

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