# commute

1. ### problem with commute matrices

hi all, i need to prove that if a square matrix commutes with any square matrix (with the same dimensions of course) than it must be a scalar matrix. appriciate the help.
2. ### Exact Sequences - Diagrams that 'commute' - Example

I am reading Dummit and Foote Section 10.5 on Exact Sequences. I am trying to understand Example 1 as given at the bottom of page 381 and continued at the top of page 382 - please see attachment for the diagram and explanantion of the example. The example, as you can no doubt see, requires an...
3. ### Exact Sequences - Diagrams that 'commute' - vertical arrows

I am reading Dummit and Foote on Exact Sequences and some of the 'diagrams that commute' have vertical arrows. Can someone please help me with the LaTex for these diagrams. I have given an example in the attachment "Exact Sequences - Diagrams with Vertical Arrows" - where I also frame my...
4. ### Subspaces containing matrices that commute with a given matrix

Problem: Determine the subspace of R(2 by 2) consisting of all matrices that commute with the given matrix: (1 0 ) =B (0 -1) Attempt at sol'n: I wanted a general 2 by 2 matrix A so that AB=BA. Multiplying out component wise, I think that it must be the case that a11=a11, a12=-a12=0...
5. ### prove that distinct reflections commute iff...

let m and l be lines in E_2, and the reflection of l is the mapping \Omega_l of E_2 to E_2 defined by \Omega_lX = X - 2N((X - P) \cdot N) where N is the unit normal to l and P is any point on l Show that two distinct reflections \Omega_l and \Omega_mcommute if and only if m \perp l.
6. ### Find all matrices {(a,b);(c,d)} that will commute with every matrix in set S

where set S is the set of all 2x2 matrices so i set an arbitrary matrix from the set S {(w,x);(y,z)} so (sorry i dont know the matrix format :< ) [a b][w x] = [w x][a b] [c d][y z] [y z] [c d] and got [(ax+bz) (ay+bw)] = [(xa+yc) (xb+yd)] [(cx+dz) (cy+dw)] =...
7. ### Proving that matrices commute

1) A and B are n x n matrices and A is invertible. Show that (A+B)A^-1(A-B) = (A-B)A^-1(A+B) 2) A and B are n x n invertible matrices that commute. Show that A^-1 and B^-1 also commute
8. ### Proving that matrices commute

a) A, B and C are n x n matrices such that AB= I and CA = I. show that B = C. b) A and B are n x n matrices that commute i) show that A^2 and B^2 commute. ii) Give a generalization of this result.
9. ### AB=A+B;Prove A and B commute

If A and B are two square matrices of the same order such that AB=A+B then prove that A and B commute i.e. AB=BA
10. ### Give an example of rotations do not always commute in plane

Give an example of t wo rotations in the plane which proves that rotations do not always commute.
11. ### Cost to commute equation?

I was just curious, but what would an equation look like to figure out how much a commute costs factoring in the following variables: cost of gas, length of commute, and average mpg?
12. ### Commuting Homomorphisms

Let phi: R-->R' be a ring homomorphism, I an ideal of R, J an ideal of R' and suppose that phi(I) is a subset of J. Let f and g be the natural homomorphisms, f:R-->R/I and g:R'-->R'/J defined by, f(r) = r+I for all r in R and g(r')=r'+J for all r' in R'. Now, define a homomorphism h:R/I-->R'/J...
13. ### Prove that Disjoint cycles commute

Question: if f and g in Sn are disjoint cycles fg = gf Answer: f = (a1 a2 a3... an) g = (b1 b2 b3 ... bm) where ai != bj for any i or j gf(ai) where i = 1 to n-1 gf(ai) = g(ai+1) = ai+1 fg(ai) = f(ai) = ai+1 thus f and g commute for ai where i = 1 to n-1 this same method can be used to show...