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 .

If A is a non - singular matrix then

If a non-singular matrix A is symmetric ,show that A^(-1) is also symmetric

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.

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.

If A is a non-singular matrix, prove that (a d j\ A)^(-1)=(a d j\ A^(-1)) .

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

Column I, Column II If A is an idempotent matrix and I is an identity matrix of the same order, then the value of n , such that (A+I)^n=I+127 is, p. 9 If (I-A)^(-1)=I+A+A^2++A^2, then A^n=O , where n is, q. 10 If A is matrix such that a_(i j)-(i+j)(i-j),t h e nA is singular if order of matrix is, r. 7 If a non-singular matrix A is symmetric, show that A^(-1) . is also symmetric, then order A can be, s. 8

Let A be a non-singular square matrix of order n. Then; |adjA| =

If A is a non-singular square matrix such that |A|=10 , find |A^(-1)|