Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

determine if the following matrices are similar, if yes, prove it. \begin{pmatrix} 2 & 1 \\ 0 & 2 \\ \end{pmatrix} \begin{pmatrix} 2 & 0 \\ 0 & 2 \\ \end{pmatrix}

I checked some shared properties between similar matrices, such as determinant, characteristic polynomial and trace. Everything seems fine, I guess they are similar, but how to prove this? Thank you in advance.

share|improve this question
Hint: What happens if you express the second matrix on another basis? –  Marc van Leeuwen Apr 2 '13 at 16:44
add comment

2 Answers 2

up vote 3 down vote accepted

Note that the second matrix is $2I$. IF the two matrices are similar, then $\pmatrix{2&1\\ 0&2}=P(2I)P^{-1}$ for some invertible matrix $P$. Now, do you know what is $P(2I)P^{-1}$ equal to?

share|improve this answer
yes, $2I$, got it. thank you –  user63219 Apr 2 '13 at 16:44
add comment

They are not similiar, cause you can't diagonalize the first one, as you only find one eigenvector, but the second one is already diagonal.

share|improve this answer
thank you so much –  user63219 Apr 2 '13 at 16:42
add comment

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

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