Let m,(k) denote the space of all nxn matrices with entries from afield k. fix a non-singular matrix a=(4;) €m,(k) and the consider linear map t:m,(k)>m,(k) giv

Let M,(K) denote the space of all nxn matrices with entries from afield K. Fix a non-singular matrix A=(4;) €M,(K) and the consider linear map T:M,(K)>M,(K) given by: T(X)= AX. Then (a.) Trace (T)=n2jdi (b.) Trace (T)=Zi 24 (c.) Rank of T is n (d.) T is non-singular