shearing matrix is orthogonal matrix?

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Shearing matrix is orthogonal matrix?

Here is a 2D shearing matrix.

H(s) = |1  s|
       |0  1| 

No, this matrix is not orthogonal if s is nonzero. An orthogonal matrix has orthogonal rows and columns, but the dot product of the first and second row is s, and so if s is nonzero the matrix is not orthogonal.

More generally, orthogonal matrices represent rigid transforms. A shear is not a rigid transform, since it distorts one of the axes in relationship to the other.

Only if s=0.

Indeed, for it to be orthogonal you much have 1^2+s^2 = 1 and 0^2 + 1^2 = 1, i.e. s^2 = 0.