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$A^2=AB+BA$. Prove that $\\det(AB-BA)=0$ - Mathematics Stack Exchange Let A, B A, B be two 3 × 3 3 × 3 matrices with complex entries, such that A2 = AB + BA A 2 = A B + B A Prove that det(AB − BA) = 0 det (A B − B A) = 0 Nice problem, and I want to find a solution AB − BA = A2 − 2BA = (A − 2B)A A B − B A = A 2 − 2 B A = (A − 2 B) A so if |A| = 0 | A | = 0 we have done, if |A| ≠ 0 | A | ≠ 0 I can't prove
How many $4$-digit palindromes are divisible by $3$? How many 4 4 -digit palindromes are divisible by 3 3? I'm trying to figure this one out I know that if a number is divisible by 3 3, then the sum of its digits is divisible by 3 3 All I have done is listed out lots of numbers that work I haven't developed a nice technique for this yet
How to calculate total combinations for AABB and ABBB sets? Although both belong to a much broad combination of N=2 and n=4 (AAAA, ABBA, BBBB ), where order matters and repetition is allowed, both can be rearranged in different ways: First one: AABB, BBAA,
matrices - When will $AB=BA$? - Mathematics Stack Exchange Given two square matrices A, B A, B with same dimension, what conditions will lead to this result? Or what result will this condition lead to? I thought this is a quite simple question, but I can find little information about it Thanks
Find a generating function for the number of strings The string AAABBAAABB A A A B B A A A B B is a string of ten letters, each of which is A A or B B, that does include the consecutive letters ABBA A B B A Determine, with justification, the total number of strings of ten letters, each of which is A A or B B, that do not include the consecutive letters ABBA A B B A
How to show that - Mathematics Stack Exchange Let A and B be two 3 × 3 matrices with complex entries such that A2 = AB + BA Prove that det (AB − BA) = 0 (Is the above result true for matrices with real entries?)
linear algebra - $AB+BA= (trB)A + (trA)B + (trAB - trAtrB)I_2 . . . I've tried to prove the assertion considering arbitrary two matrices A, B A, B in M2(F) M 2 (F) I have calculated AB A B and BA B A Then, I have obtained the equality above However, it is too long and boring Is there any short way?