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I obtained the same result. Thank you very much :) Also, my bad. The "given" part in the 3rd question is not given. The question is written as follows: A, B and C are three matrices of order 2x2. Prove that C (AB-BA) ^2= (AB-BA) ^2*C. You can use the results obtained in parts 1 and 2 in order...

[MHB thread moved to the PF schoolwork forums by a PF Mentor] For every square matrix A, C=A(A^t)+(A^t)A is symmetric.

Yes. I apologize.

Thank you very much for the response, sir. In regard to #2 -- I calculated AB-BA. However, I did not see how the sum of the two entries in the diagonal equal zero. I obtained the following entries: a11= rb-cp a22=qc-dp How should I proceed?

If A and B are matrices that AC = AC and BC=CB, where C is a matrix whose first row's entries are 0 1 and the second row's entries are -1 0, then AB=BA.

1. A is a matrix of order 2x2 whose main diagonal's entries' sum is zero. Prove that A^2 is a scalar matrix. 2. Given: A and B are two matrices of order 2x2. Prove that the sum of the entries of the main diagonal of AB-BA is zero. 3. A, B and C are three matrices of order 2x2. Given: A^2 is a...