ag.algebraic geometry - Lie bracket on the unshifted tangent complex?

Matrices that commute with parts of particular linear group Answer

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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.

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

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

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

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