# Is this the correct application of model transformation?

Suppose I want to perform translate in the following order:

1. Scale by $S$
2. Rotate by matrix $R_1$
3. Rotate by matrix $R_2$
4. Translate by $T%$.

When I apply the matrix, should the overall transformation matrix be:

$M = T \times R_1^{-1} \times R_2^{-1} \times S$

or

$M = T \times R_2^{-1} \times R_1^{-1} \times S$ ?

I always thought the transformations should be applied in reverse, so it should be the second case. But I'm told that it's the first case instead. Is there a special need to reverse the order of rotation apart from taking the inverse too?

By the way, why must I take the inverse matrix for rotation?

• Matrices can be row or column major which flips the order that you would apply them in. There's no need to inverse any rotations to accomplish a rotation. – Andrew Wilson Jan 14 '18 at 4:30
• Whoever told you the first case is confused and you are too. The overall transformation matrix, assuming it will be applied to the left of a column vector, should be $M=TR_2R_1S$. – Rahul Jan 14 '18 at 11:48