## Chapter 01. Matrices, Vectors, and Vector Calculus

### Problem 04. Transposed and Inverse Matrix

##### The problem asks you to

prove the properties of transposed and inverse matrix.

##### You should know about

1) Transposed matrix 2) Inverse matrix

##### Solution

(a) Let , then By definition of transpose, Therefore,

(b) i) For orthogonal matrices, , so we can use the result of (a). ii) For non-orthogonal matrices (i.e. In general), Therefore,