# Normalize transformation matrix with inverse scale

I am attempting to export a transformation matrix from the API of a design program. The matrix looks fine and it is workable apart from 1 issue where the scaling factor is inverse. This means when you scale down a shape it results in a scaling factor > 1 and vice versa.

For example, following matrix $$\begin{bmatrix}2&0\\0&2\end{bmatrix}$$ Results in the shape being twice as small.

Now I am trying to use this matrix and apply it somewhere else, but because of the inverse scale I am unable to use it. Is there any way to normalize the scaling factor of a affine transformation matrix?

One last thing to note is the fact that the rotation applied, according to documentation is also reversed from standard formulas. Their rotation matrix would look something like this: $$\begin{bmatrix}cos&sin\\-sin&cos\end{bmatrix}$$

• Can you just invert the matrix? May 15 '20 at 11:39
• @Hume2 ugh you were right, inverse matrix worked fine.You post it as answer if you want. May 16 '20 at 7:12

When the matrix is unitary (your second example), it holds that $$A^{-1}=A^T$$. All rotation matrices are unitary and in the case of 2D rotation matrices, it's clear that the inverse has to be the backwards rotation.