Which Matrices Satisfy AB=BA for A=[1 0; 1 1]?

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To find matrices B that satisfy the equation AB = BA for A = [1 0; 1 1], one must express B in the form B = [a b; c d]. By multiplying both sides of the equation AB and BA, constraints on the variables a, b, c, and d can be derived. The discussion emphasizes the importance of calculating the product of A and B to identify these constraints. Additionally, the role of the inverse of matrix A in this context is questioned, highlighting its relevance in understanding the relationship between the two matrices. Ultimately, the solution requires careful algebraic manipulation of the matrix equations.
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I would appreciate if someone could help me with this one.

Matrix A=[1 0 ; 1 1]
I need to find all matrices that satisfy: AB=BA
How can I find them?
PLease help :cry:
 
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Try writing
B=\left(\begin{array}{cc}a & b \\ c&d \end{array}\right)

and check what the constraints on a,b,c and d are.
 
did that. And put A(inverse)* [a b;c d] = C*A(inverse)
 
What does the inverse have to do with everything...?

Daniel.
 
yea, just write out AB=BA using B=[a,b;c,d] and A=[1,0;1,1]
and multiply out both sides.
 
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