I try to identify the corresponding shearing transformation using its matrix form based on the description here:

In[376]:= Clear[x,y,z];
m={x\[Minus]y, x, z}//CoefficientArrays//Normal//Last
% . {x,y,z}

Out[377]= {{1, -1, 0}, {1, 0, 0}, {0, 0, 1}}

Out[378]= {x - y, x, z}

I try to figure out the geometric meaning corresponding of the above matrix m in terms of the shearing transformation defined in Wolfram language. I tried a few examples like the one below, but none of the results corresponded exactly to the matrix form above:

In[405]:= ShearingMatrix[-Pi/4,{1,0,0},{0,0,1}]
ShearingMatrix[-Pi/4,{0,1,0},{0,0,1}]
ShearingMatrix[-Pi/4,{0,0,1},{0,1,0}]
ShearingMatrix[-Pi/4,{1,0,0},{0,1,0}]

Out[405]= {{1, 0, -1}, {0, 1, 0}, {0, 0, 1}}

Out[406]= {{1, 0, 0}, {0, 1, -1}, {0, 0, 1}}

Out[407]= {{1, 0, 0}, {0, 1, 0}, {0, -1, 1}}

Out[408]= {{1, -1, 0}, {0, 1, 0}, {0, 0, 1}}

Any tips for solving this problem?

Regards,
Zhao