# Re: [xmca] a minus times a plus

```re: Ed Wall message to Michael about matrices.

Here's the modern math-talk about it:-

If  _a_ is a 3D transformation/function/mapping represented by square matrix A,
and _b_ is a 3D transformation/function/mapping represented by square matrix B,

then the composite function _a_ @ _b_ ("_b_ followed by _a_" or the
other way round, depending on convention but stick to that convention)
is represented by the matrix AB.  functions and matrices are non-commutative
in general. but since
det(AB) = det(A) det(B)
the determinant map det:A |---> det A defines a homomorphism from
square matrices to the integers.  this is where you "lose"
non-commutativity.  although AB is not the same as BA in general,
det(AB) = det(A) det(B) = det(B) det(A) = det(BA)
when you are back to the numbers-world from your excursion into the
Matrix world,
the commutative law operates again.

Foo Keong
NIE, Singapore
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```