Let A be any ` 3xx 2` matrix show that AA is a singular matrix.

If A is a non - singular matrix then

Let A be a matrix such that A* [(1 ,2) ,(0 ,3)] is a scalar matrix and |3A|=108 .Then A^(2) equals

If A is any mxxn such that A B and B A are both defined show that B is an nxxm matrix.

Let A be a non-singular matrix. Show that A^T A^(-1) is symmetric if A^2=(A^T)^2

Let A be a non-singular matrix. Show that A^T A^(-1) is symmetric iff A^2=(A^T)^2 .

Let A be any 3xx2 matrix. Then prove that det. (A A^(T))=0 .

For, a 3xx3 skew-symmetric matrix A, show that adj A is a symmetric matrix.

Let A be a 3xx3 matrix such that A^2-5A+7I=0 then which of the statements is true

If A and B are any two 2 xx 2 matrices such that AB=BA=B and B is not a zero matrix, what can you say about the matrix A ?

Let A be a square matrix. Then prove that (i) A + A^T is a symmetric matrix, (ii) A -A^T is a skew-symmetric matrix and (iii) AA^T and A^TA are symmetric matrices.