Please prove the following question. Let A=(a_(ij))_(i)=1,2,dots,m;j=1,2,dots,n=(a_(1),a_(2),dots,a_(n)) be a matrix whose all components are real numbers,
where a_(1),a_(2),dots,a_(n) are column vector of A. Then prove that tr(A^(')A)=0 holds if and only if A is the
zero matrix. (15 points)
where a1,a2,...,an are column vector of A. Then prove that tr(A'A) = 0 holds if and only if A is the zero matrix. (15 points)