@acer : Thank you a lot!

@dharr : Thank you

@dharr : It's just not true for powers of 2, is it?

@Carl Love :
Wow! Your counter-example is absolutely correct. 

However I solved it like this: 

Since matrix B is invertible, there exists its inverse matrix B^-  . We have: (A.B^-)²⁰²³= A²⁰²³.(B^-)²⁰²³=0 
deduce: C = A.B^-  is nilpotent , so, ==> I- A.B^-  invertible. (according to part a).
==> (I- A.B^-).B = B-A invertible (because the product of two invertible matrices is invertible).
Please help me point out the error in my argument!
Thank youso much!

@Carl Love : I solved it. Thank you again!

@Carl Love : Could you help me further, about part b?

@Carl Love : Thank you a lot for your suggestion.

@vv 

I can solve that problem by hand, but can't write commands to solve it with Maple.

@Carl Love 

I think they want to test skills in manipulating the properties of powers (a^m*a^n=a^(m+n))(?). I myself forgot to use this feature at first, so I encountered difficulty in solving problems.

@Carl Love 

Thank you very much! With your suggestion, I solved the problem (by hand).

@Carl Love 

It's amazing how a seemingly complicated problem can be solved so simply! Thank you so much for your help!

@Kitonum 

Sorry! If the bound of the integral is 1..2 (int(x*f(x), x=1..2) then I really have a trick to solve it quickly without using Maple (using a constant function). Issue is here that I don't dare to assert that the requirement to compute primitives with bounds of 2..3 is not satisfactory. Thank you again.

@Kitonum 

Thank you very much! I also thought there was a problem with the assumptions of the problem (the bounds of the integrals are not equivalent). But because my level of math is limited, I dare not boldly assert.

@rlopez 

Great! Thank you very much! Although I understand the problem you have explained, but due to skill limitation, I am not able to write the complete statement of command. Can you help me, for this particular case? Sorry if I have bothered. Thank you very much!

@vv 

Thank you! Now I understood!