Pre and Post Multiplication World Space Transform Matrix ambiguity

I'm presently studying astir world abstraction translator matrices and encountered immoderate disorder regarding their exertion successful different matrix orders (row awesome vs file major).

Context

In statement awesome order, a constituent is represented arsenic \begin{bmatrix} x,y,z \end{bmatrix} In file awesome order, nan aforesaid constituent is represented as \begin{bmatrix} x \\ y \\ z \end{bmatrix}

World Space Transformation

For file awesome order, we usage post-multiplication: $P1 = WST * p1 = S * Rx * Ry * Rz * T * p1$

For statement awesome order, it's we usage pre-multiplication: $P2 = p2 * WST = p2 * T * Rz * Ry * Rx * S'$

However, I feel, for statement awesome it should alternatively be: $P2 = p2 * WST' = p2 * T' * Rz' * Ry' * Rx' * S'$ wherever ' denotes transpose of nan matrix.

My Reasoning

Both P1 and P2 correspond nan aforesaid transformed point, conscionable successful different orders (column awesome vs statement major).

So, $P2 = P1' = (S * Rx * Ry * Rz * T * p1)'$

Since, $(AB)' = B'A'$

We tin opportunity that, $P2 = p1' * T' * Rz' * Ry' * Rx' * S' = p2 * T' * Rz' * Ry' * Rx' * S'$ (as $p1' = p2$)