Common Geometric Transformation Matrices

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Transformation	Matrix
Scaling by factor $k$	X Axis: $\left[\begin{array}{cc}k& 0\\ 0& 1\end{array}\right]$ Y Axis: $\left[\begin{array}{cc}1& 0\\ 0& k\end{array}\right]$
Rotation by $\theta$	Clockwise: $\left[\begin{array}{cc}\cos (\theta )& \sin (\theta )\\ -\sin (\theta )& \cos (\theta )\end{array}\right]$ Anticlock.: $\left[\begin{array}{cc}\cos (\theta )& -\sin (\theta )\\ \sin (\theta )& \cos (\theta )\end{array}\right]$
Reflection	X Axis: $\left[\begin{array}{cc}1& 0\\ 0& -1\end{array}\right]$ Y Axis: $\left[\begin{array}{cc}-1& 0\\ 0& 1\end{array}\right]$
Reflection along line	$y=x:\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]$ $y=-x:\left[\begin{array}{cc}0& -1\\ -1& 0\end{array}\right]$
Shearing by factor $k$	X Axis: $\left[\begin{array}{cc}1& k\\ 0& 1\end{array}\right]$ Y Axis:$\left[\begin{array}{cc}1& 0\\ k& 1\end{array}\right]$