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# Let A and Bbe similar n X n matrices. Show that A and B have the same characteristic polynomial. (Hint: suppose that S is an n X n invertible matrix s0 that A = SBS...

## Question

###### Let A and Bbe similar n X n matrices. Show that A and B have the same characteristic polynomial. (Hint: suppose that S is an n X n invertible matrix s0 that A = SBS-1 Note that A AIn SBS-I AIn = S (B AI,) $-1 Take the determinant; and use property of determinants (a theorem in Section 4.2)) What does the previous part imply about the eigenvalues of Aand B? What does the first part imply about the trace and determinant of A and B? 31 126 Use the previous part to show that that 10 is not similar t Let A and Bbe similar n X n matrices. Show that A and B have the same characteristic polynomial. (Hint: suppose that S is an n X n invertible matrix s0 that A = SBS-1 Note that A AIn SBS-I AIn = S (B AI,)$-1 Take the determinant; and use property of determinants (a theorem in Section 4.2)) What does the previous part imply about the eigenvalues of Aand B? What does the first part imply about the trace and determinant of A and B? 31 126 Use the previous part to show that that 10 is not similar to 21 21 ~10  #### Similar Solved Questions

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