MATRICES IN VERY EASY WAY

Show that A' A and A A' are both symmetric matrices for any matrix A.

Give an example of three matrices A ,\ B ,\ C such that A B=A C but B!=C .

Give an example of three matrices A ,\ B ,\ C such that A B=A C but B!=C .

Let a be square matrix. Then prove that A A^(T) and A^(T) A are symmetric matrices.

A: ELISA can enable very easy detectron of infection through antigen antibody interaction. R : It is a nucleic acid based diagonostic tool that can confirm presence of infectious microbe at early stages.

If matric A is skew-symmetric matric of odd order, then show that tr. A = det. A.

A ,\ B are two matrices such that A B and A+B are both defined; show that A ,\ B are square matrices of the same order.

Find the adjoint of the following matrices: [(-3, 5),( 2, 4)] Verify that (a d j\ A)A=|A|I=A(a d j\ A) for the above matrices.

If A and B are symmetric matrices of same order, then AB - BA is a