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i try to solve Linear algebra question(but need be written properly as mathmatical proofs)

Having A matrice nXn:

1)proove that if A^2=0 the columns of matrice A are vectors in solution space of the system Ax=0 (x and 0 are vectors of course),and show that p(A)>=n/2

2)proove that if p(A^2)<p(A) (p in all cases here means: the rank of the vectors)

so the system Ax=o has a non trivial solution and the System A^2x=0 has solution y which is Ay≠0,,,,

I have the general clue but how write it right,math way i have big problem..

thank you very much

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# Linear Algebra problem

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