Can anyone help me to understand what is suppose to do in this question?

"A matrix that is similar to the identity matrix" I should say something about this but I do not understand what is meant to do.

I know that two n x n matrices A and B are similar if $B=P^{-1}AP $.

They also have some properties such as:

The same:

Rank; Characteristic equation; Determinant; Trace; Eigenvalues etc.

However I do not understand the question and consequently I do not know how to start.

Can anyone help me on this?


  • 1
    $\begingroup$ What is the question, exactly? ("A matrix that is similar to the identity matrix" isn't a question . . .) $\endgroup$ – Noah Schweber Feb 18 '17 at 18:07
  • $\begingroup$ You mean, you're asked to calculate $P^{-1} I P$, where $I$ is the identity matrix? $\endgroup$ – Andreas Caranti Feb 18 '17 at 18:11
  • $\begingroup$ it only says. to say something about a matrix that is similar to the identity matrix. I really do not understand what should I do. $\endgroup$ – user290335 Feb 18 '17 at 18:42

A matrix $A \in M_n(\mathbb{F})$ that is similar to the identify matrix $I_n$ must be in fact the identify matrix (that is, $A = I_n$). To see why, note that if $A$ is similar to $I_n$ then we can find an invertible $P$ such that $$A = P^{-1} I_n P = (P^{-1} I_n) P = P^{-1} P = I_n. $$

  • $\begingroup$ Thank you very much for your help. $\endgroup$ – user290335 Feb 18 '17 at 22:14

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.