4x4 matrix multiplication order

Question

I"m using the following library:

https://github.com/greggman/tdl/blob/master/tdl/math.js

however, the question is about different results i'm getting when i take the same steps in different ways:

//Example 1
m = tdl.math.matrix4.identity();
tdl.math.matrix4.rotateX( m, 90*(Math.PI/180 ) );
tdl.math.matrix4.translate( m, [10,20,30]);

console.log (m); //output down below 1

//Example2
i = tdl.math.matrix4.identity();
r = tdl.math.matrix4.rotationX( 90*(Math.PI/180 ) );
t = tdl.math.matrix4.translation( [10,20,30] );
m = tdl.math.matrix4.mul( i, r );
m = tdl.math.matrix4.mul( m, t );

console.log( m ); // output down below 2

Both ways have the same order of actions, namely

1. identity
2. rotate 90 deg around x
3. translate by 10x, 20y

However, the output is not the same, here is output 1:

 [1, 0, 0, 0, 0, 6.123233995736766e-17, 1, 0, 0, -1, 6.123233995736766e-17, 0, 10, -30, 20.000000000000004, 1]

here is output 2

 [1, 0, 0, 0, 0, 6.123233995736766e-17, 1, 0, 0, -1, 6.123233995736766e-17, 0, 10, 20, 30, 1]

Why is the outcome different, when i'm seemingly taking the same steps?

Answer 1

Because multiplication of matrices is different depending on which matrix is on the left. In other words

matA * matB != matB * matA

Try

i = tdl.math.matrix4.identity();
r = tdl.math.matrix4.rotationX( 90*(Math.PI/180 ) );
t = tdl.math.matrix4.translation( [10,20,30] );
m = tdl.math.matrix4.mul( r, i );
m = tdl.math.matrix4.mul( t, m );

console.log( m ); // output down below 

Outputs

[1, 0, 0, 0, 0, 6.123031769111886e-17, 1, 0, 0, -1, 6.123031769111886e-17, 0, 10, -30, 20.000000000000004, 1]