This may seem like a simple question, but I can't wrap my head around it, and I haven't been able find the answer on the web.
The formula for rotating a point, defined by the vector $\vec{x}$, around another point, defined by the vector $\vec{x_0}$, with an angle, $\theta$, given by the rotation matrix, $A_\theta$, is:
$D(\vec{x}) = A_\theta(\vec{x}-\vec{x_0}) + \vec{x_0}$
I get the logic behind this, but now I am to proof that the expression above is the same as:
$D(\vec{x}) = A_\theta\vec{x} + (I_2 - A_\theta)\vec{x_0}$
Can some of you tell me how I get from the first expression to the second expression?
Thanks!