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

For any matrix a show that A+A^(T) is symmetric matrix

Let A be a square matrix. Then prove that A + A ^(T) is a symmetric matrix.

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

Let A be a square matrix. Then prove that A - A^(T) is a skew-symmetric matrix

Let A be a square symmetric matrix. Show that 1/2 (A+A') is a symmetric matrix.

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^(T)A are symmetric matrices.

Let A be a square symmetric matrix. Show that 1/2 (A-A') is a skew-symmetric matrix.

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.