# Thornton & Marion, Classical Dynamics, 5th Edition

## Chapter 1. Matrices, Vectors, and Vector Calculus

### Problem 04. Transposed and Inverse Matrix

#### The problem asks you to

- prove the properties of the transposed and inverse matrix.

#### You should know about

- Transposed matrix
- 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,