Q3Multiple correct2 Marks24 Mar 2024Select all true statements.AAAA and BBB are square matrices of order nnn. If rank(A)=k\operatorname{rank}(A)=krank(A)=k, with k≤nk\le nk≤n, and rank(B)=n\operatorname{rank}(B)=nrank(B)=n, then rank(AB)=k\operatorname{rank}(AB)=krank(AB)=k.BThe rank of a matrix is equal to the maximum number of linearly independent columns.CThe rank of a diagonal matrix is equal to the number of diagonal entries that are zero.DFor a matrix AAA of dimensions m×nm\times nm×n, rank(A)+nullity(A)=m\operatorname{rank}(A)+\operatorname{nullity}(A)=mrank(A)+nullity(A)=m.
