The value stored in Out
is, as a rule, what is displayed in the output. The only exception from that are the various *Form
s, MatrixForm
being an example of that. When one of such "wrappers" (as the help calls it) is detected in the top level of the output, it is removed from the expression prior to assigning to Out
. The front end makes it clear that what's displayed is not the value of Out
:
In[1]:= {{1,2},{0,1}} // MatrixForm
Out[1]//MatrixForm= 1 2
^^^^^^^^^^
0 1
In[2]:= Out[1]
Out[2]= {{1, 2}, {0, 1}}
The reason for this is that it's convenient for further processing of the output. The MatrixForm
itself would be inoperable:
In[3]:= ({{1,2},{0,1}} // MatrixForm) * 2
Out[3]= 2 1 2
0 1
One would need to manually remove the outer layer every time of using Out[]
as the price for wanting to have the output nicely displayed. So Mathematica does that for the user as a convenience.
In your example you assigned MatrixForm[mA]
to mfA
so that's what mfA
is. (This is often exactly the undesirable behaviour.) As a result of the assignment, MatrixForm[mA]
is printed. But now the rule gets applied, the top-level MatrixForm
is shaved, and only mA
stored in Out
for that input line.
Update: the list of functions which behave as wrappers is $OutputForms
, as found here:
? $OutputForms
$OutputForms
is a list of the formatting functions that get stripped off when wrapped around the output.
You can unprotect it, add or remove some (or all of them) and cause MatrixForm
to be stored in the Out
or StringForm
not to:
In[1]:= Unprotect[$OutputForms];
In[2]:= $OutputForms = {StringForm};
In[3]:= {{1,2},{0,1}} // MatrixForm
Out[3]= 1 2
0 1
In[4]:= % + 2
Out[4]= 2 + 1 2
0 1
In[5]:= "abc" // StringForm
Out[5]//StringForm= abc
^^^^^^^^^^
In[6]:= Head[%]
Out[6]= String