Hi,

As Gianluca pointed out, MatrixForm is for display only. Multiplication of matrices is done with them in their "raw" form. The result of the multiplication could be displayed by applying MatrixForm to it. Since it looks better than the raw List-of-Lists form. But the MatrixForm version of the product will no be suitable for further computations. Use the raw product if you want to carry on with calculations. Please see the attached.

Attachments:

The use of MatrixForm is tricky. You should use it only for display, and not for calculation. One way of doing that is to wrap the assigment in parentheses (), and only thereafter use MatrixForm, i.e.: (a={{1,0},{0,1}})//MatrixForm, instead of a={{1,0},{0,1}})//MatrixForm, or else separate entirely the assignment and the display:

a = {{1, 0}, {0, 1}};
a // MatrixForm

We all hope that Wolfram Research will soon make these obscure tricks obsolete by a revision of MatrixForm.