If i understand what you said correctly, if two matrices (A and B) together; to find element 2,3 of the resulting matrix

Row major multiplication: take the dot product row 2 of matrix A and column 3 of matrix B

Column major multiplication: take the dot product of column 2 of matrix A, and row 3 of matrix B

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So, last question (i hope). Does the above mean that the formula for matrix product (For matrices F & G):

This will always take dot product the i-th row and j-th column of the two matrices, the only difference being that row major = FG, while column major = GF

OR, do the subscripts get a different meaning? Like in row major it's the i-th row and j-th column, where with column major it's the j-th row and i-th column?

If i understand correctly, the transpose is a result of treating the vector as a column vector; hence the matrix is never actually transposed. Is that correct?

I have one more question regarding pre / post multiplication. I always assumed that the whole row v column order was what determined if pre or post multiplication is used (Due largely to my understanding of linear algebra being based on the differences in OpenGL & Direct X).

Now that i'm trying to build some more solid mathematical foundations i find my old understanding very chalenged.

If we have Matrix T (a translation matrix that translates by 10, 20 and 30)

and matrix S (A scale matrix that is a uniform scale of two)

And we want to concatinate the transformation so that the matrix translates first, and scales second we must calculate it as S x T.

This is assuming the same multiplication method as in the first post. I think because we scaled first then translated this is using post multiplication?

If correct, how come post multiplying two row major matrices works in math but Direct 3D uses pre-multiplication? Is this due to some implicit like the vector X matrix multiplication? Am i missing something trivial in my mental model of how this works?

Or perhaps is my pre / post terminology wrong when it comes to multiplying matrices?

It's just in blender. You're gonna have to do some googling. Tough as phantom pointed out, UE4 man! Should be super quick to prototype with blueprints.