# Matrices that commute with parts of particular linear group Answer

Hello pricey customer to our community We will proffer you an answer to this query Matrices that commute with parts of particular linear group ,and the respond will breathe typical by documented data sources, We welcome you and proffer you fresh questions and solutions, Many customer are questioning in regards to the respond to this query.

Matrices that commute with parts of particular linear group

Given a matrix
$$M=commence{bmatrix} w&x y&z aim{bmatrix}inmathbb Z^{2times2}$$ with $$wz-xy=1$$ is there an outline of $$2times2$$ matrices $$U$$ such that $$UM=MU$$?

This is what I get.

$$commence{bmatrix} a&b c&d aim{bmatrix}commence{bmatrix} w&x y&z aim{bmatrix}=commence{bmatrix} w&x y&z aim{bmatrix}commence{bmatrix} a&b c&d aim{bmatrix}$$

$$commence{bmatrix} aw+by&ax+bz cw+dy&cx+dz aim{bmatrix}=commence{bmatrix} aw+cx&bw+dx ay+cz&by+dz aim{bmatrix}$$

$$commence{bmatrix} by-cx&ax+bz-bw-dx cw+dy-ay-cz&cx-by aim{bmatrix}=commence{bmatrix} 0&0 0&0 aim{bmatrix}$$

we’ll proffer you the answer to Matrices that commute with parts of particular linear group query through our community which brings all of the solutions from a number of dependable sources.