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

If A is a non-singular symmetric matrix, write whether A^(-1) is symmetric or skew-symmetric.

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 skew-symmetric matrix then A^(2) is a symmetric matrix.

If A is a symmetric matrix ,then prove that adj A is also symmetric

A matrix which is both symmetric as well as skew-symmetric is

If A is a matrix such that A^2+A+2I=Odot, the which of the following is/are true? (a) A is non-singular (b) A is symmetric (c) A cannot be skew-symmetric (d) A^(-1)=-1/2(A+I)

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

If A is a square matrix, then A is skew symmetric if

If A is a non-singular matrix, prove that: a d j\ (A) is also non-singular (ii) (a d j\ A)^(-1)=1/(|A|)Adot