# Question:Matrix over noncommutative elements - Physics Package

## Question:Matrix over noncommutative elements - Physics Package

Maple

I tried to use the Physics package in maple 13 to make operations in the algebra M_2(E) - the algebra of 2x2 matrices over the grassmann (or exterior) algebra. E is a noncommutative algebra, and some of its elements anticommute with each other.

The problem is that when I multiply such matrices, the answer is not right. Maple multiply this matrices considering the entries as commutative, what is not true.

Here are the commands I used:

> with(Physics);
> Setup(anticommutativeprefix = {Yc, y});
> C[1] := Matrix([[X[1], Y[1]], [y[1], x[1]]]);
> C[2] := Matrix([[X[2], Y[2]], [y[2], x[2]]]);
> Physics[`.`](C[1], C[2]);
> Physics[`.`](C[2], C[1]);

and what I get after

> Physics[`.`](C[2], C[1]);

is not right (Maple commutes y[1] with Y[2])

How can I solve such problem? Can I multiply matrices considering that its entries are non commutative and get right answers?

Thanks for helping!

Thiago.

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