# identity matrix

#### kokkie_d

Joined Jan 12, 2009
72
Hi,

I have the following function:
$$f(x) = e^{\underline{A}t}*\underline{A}^{-1}*\underline{A}*e^{\underline{A}T-t}$$
Where $$\underline{A}$$ is A matrix.

Am I allowed to simplify $$\underline{A}^{-1}*\underline{A}$$ to an identity matrix?

I know a matrix times its inverse is an identity matrix but I am worried about the order to do the calculations in and if it then still is allowed.

Cheers

#### Georacer

Joined Nov 25, 2009
5,182
If your function is exactly as you wrote it, then you can.

The inverse matrix of $$A$$, $$A'$$ is defined as:
$$A \cdot A'=A' \cdot A=I$$