@C_R  Hi there.

Thanks for the feedback.  I think you made a supposition that may not be true: that everything that works in Maple works in MF as well. To confirm or not such a statment one should know very well both. This is not my case.

I guess your code works in Maple, but in MF for what I know things are a bit different. At least they are different in the default canvas. For instance it works the following command, you wrote:

A := Matrix(2, 2, [[0.2, 0.3], [0.5, 0.4]]);

You need an "=" sign to see the Matrix result:  

A = and in perfect Matrix form one can see the same "A" I wrote in the first post.

However the following command does not work, in the default canvas. It is perceived as simple Text:

whattype(A)

I see that among the "styles" in MF there is also a "Input Maple". Assigning that style to the above comand it changes color, but nothing else occurs (there is no Maple program in the same machine that I guess is necessary to run "Input Maple" in MF). Far less I was able to see the result by assigning a variable, let's Output1:=whattype(A),  and in the standard MF canvas, writing "Output1=", as I did before with "A=". In this case nothing comes out. 

Other thing that puzzled me was the following. While I was searching for a solution in the MF "help" file, I was sent to the online page here: 

https://www.maplesoft.com/support/help/Maple/view.aspx?path=LinearAlgebra

Among the page examples, I found commands (which should be mainly for Maple, and not all for MF I think), with what I consider spurious typos that do not help at all. Here an example: 

@C_R  Thanks.

Yes,  also the command I showed gives an immediate output without delay. However, I found unusual the behaviour of MF, given that it wants to be with a friendly interface as MC. And the strangeness is not only that it does not give an answer, but that - if that type of summation was forbidden - it attempts the calculation (freezing for a while the software), and throwing that kind of feedback seen on the picture.

PS: I tried to insert your command (not easy, since after "i=" the cursor jumps back):

EXPP_A := sum(Aⁱ, i=0..1) 

but the feedback from MF is the same of the summation symbol: the software freezes for sometime (very deprecated reaction) and then it gives the same feedback "In Matrix too many levels of recursion". Probably one needs to open a maple input (if it is possible: I am a novel MF user), instead to just use a numeric MF input, but this is also unfriendly as compared to MC. 

I tried several alternatives, just to understand that MF does not accept Matrix exponents, using index. The above sum formula is enough to freeze the application for half a minute or so (while MF attempts to "solve" it). This seems a limitation as compared to the "friendly approach" of MC, that even with i from 0 to 50 gives an answer instantly.

What seems to work in MF is the following: leave the Sum symbol but within the brackets, instead of just Aⁱ, insert:

LinearAlgebra[MatrixPower](A, i)

@C_R  Hi there, thanks to your note.

The range is made purpously with "i" from 1 to 1, so that MF should not made any recursive sum, but it should just return as output matrix A. If I make i from 0 to 50 or any number above 1 ( as I did in MC) the message is the same, but at least in that case there are some recursive sum cycles. 

Strange thing: if the index "i" is removed from the exponent and it is made as a matrix mulitplier (i*A), using as above the same symbol Sum, there is no error. 

As it is clear from the formula EX_A the geometric series is not explosive. So the calculation (see Mathcad) is possible even with i from 0 to 50 or more. Yet in MF it does not work even with i from 1 to 1.