# how to make a matrix B such that AB=BA

by yooyo
Tags: abba, matrix
 P: 7 B is not the identity matrix or the zero matrix suppose both A and B are 3X3 I dont have clue on this..any hits?
 P: 1,076 Well write out two 3x3 matrices of variables and calculate AB, and BA set them equal to one another(element by element) and find the conditions on the entries of each matrix that make it true that AB=BA.
 HW Helper Sci Advisor P: 9,371 how abouit 2Id?
P: 7

## how to make a matrix B such that AB=BA

what do you mean by 2Id? 2xI?
 HW Helper Sci Advisor P: 9,395 There is an obvious choice for B (well infinitely many) that is not Id or 0. What will A always commute with?
 PF Patron Sci Advisor Thanks Emeritus P: 38,424 Is the question "Given B find A such that AB= BA"?
 P: 7 it is given A find B such that AB=BA.. what is the obvious choice...
 HW Helper Sci Advisor P: 2,020 A will commute with itself and all its powers. Also, A will commute with all multiples of Id.
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P: 11,722
 Quote by yooyo it is given A find B such that AB=BA.. what is the obvious choice...
B=A, or B=I.
 PF Patron HW Helper Sci Advisor P: 4,083 special polynomials in kA, where k is a constant
 HW Helper Sci Advisor P: 9,395 Uh? *any* polynomial in A commutes with A (dunno what the k has to do with anything).
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