# Thread: Inverse and Transpose of a matrix to get Identity

1. ## Inverse and Transpose of a matrix to get Identity

Hey guys,

I just want to know when an inverse or transpose of something ( vector or matrix ) will multiply a (vector or matrix) from the right or left to make it into an I.

For example,
A^TAx = b
A^-1A = I
S^-1AS

I'm having trouble when the rule applies to make something into an Identity when multiplying by an inverse or transpose.
Does it have to be square? linearly independent? singular? non singular? etc.

2. ## Re: Inverse and Transpose of a matrix to get Identity

Hey Cake.

There is a well known formula that when R*R^t = R^t*R = I then R is a rotation matrix.

3. ## Re: Inverse and Transpose of a matrix to get Identity

Originally Posted by chiro
Hey Cake.

There is a well known formula that when R*R^t = R^t*R = I then R is a rotation matrix.
When will this hold true? Is their any requirements for this to be true.

4. ## Re: Inverse and Transpose of a matrix to get Identity

You should look up rotation matrices for this.

https://en.wikipedia.org/wiki/Rotation_matrix

The derivation for this identity is something done in continuum mechanics so you should read the relevant textbooks/literature/whatever for more information.