Prove that the inverse of a symmetric nonsingular matrix is symmetric. Getting Started: To prove that the inverse of A is symmetric, you need to show that (A^-1)^T=A^-1. (i) Let A be a symmetric, nonsingular matrix. (ii) This means that A^T=A and A^-1 exists. (iii) Use the properties of the transpose to show that (A^-1)^T is equal to A^-1 | Numerade

Prove that A AT is a symmetric and A – AT is a skew symmetric matrix, where A = [52-43-724-5-3] - Mathematics and Statistics | Shaalaa.com

Symmetric Matrix & Skew Symmetric Matrix (Definition & Properties)