SOLUTION: Prove that a matrix A, 2x2 conmutes with any matrix 2x2 if and only if A conmutes with each of the matrices [1 0; 0 0], [0 1; 0 0], [0 0;1 0] [0 0; 0 1]. Find all those matrices

Question 1206243: Prove that a matrix A, 2x2 conmutes with any matrix 2x2 if and only if A conmutes with each of the matrices [1 0; 0 0], [0 1; 0 0], [0 0;1 0] [0 0; 0 1].
Find all those matrices A.
In this matrix notation a space refers to a change in column, and a semicolon to a change in row.
Thank you.
Answer by ikleyn(52855) (Show Source): You can put this solution on YOUR website!
.

Find the complete solution with comprehensive explanations under this link

https://math.stackexchange.com/questions/1107111/all-matrices-which-commute-with-all-2-times-2-matrices

RELATED QUESTIONS
Determinants: Let M = ( 𝑎 𝑐 𝑏 𝑑 ) is a 2x2 matrix. a. For which values... (answered by ikleyn)

Could you please help me to understand this q step by step? find the x value of the 2x2... (answered by rothauserc)

Give examples of the following matrices: 2x2 identity matrix I2x2(the 2x2 is smaller... (answered by longjonsilver)

If a 2X2 MATRIX A=1 0 -1 1(last 2 term in 2nd line). T hen Proved that A*A-2A+I=0. And... (answered by flame8855)

2x2 matrix A with the property A2=A A can not =I or... (answered by user_dude2008)

Let A be a 2x2 matrix. Prove that if there exists a linearly independent set of vectors... (answered by robertb)

Please help me with this word problem: Two 2x2 inverse matrices have a sum of [-2 0 ]... (answered by KMST)

We know that for scalars (real numbers) if ab = 0 then either a = 0 or b = 0. This is not (answered by KMST)

okay, i'm not very good at matrices... [4 2]____[-6 0] [5 1]*A= [-15 3] (find... (answered by stanbon)