# Identity matrix problem

#### ausmathgenius420

##### New member
Hi,
My question is if you have 2 matrices A and B, such that:
$AB=24I$How can I prove that;
$A^{-1}=\frac{1}{24}B$
Intuitively it makes sense, however my textbook doesn't provide a proof for this which I'm curious about so hopefully someone can explain.

Edit:
24I was just an example I chose. These equations can be generalised to
$AB=xI$Thus
$A^{-1}=\frac{1}{x}B$

Last edited:

#### Harry_the_cat

##### Elite Member
$$\displaystyle AB = xI$$
$$\displaystyle A^{-1} A B = A^{-1}. xI$$
$$\displaystyle IB = x A^{-1}I$$
$$\displaystyle B = x A^{-1}$$
$$\displaystyle \frac{1}{x}B = \frac{1}{x}.x A^{-1}$$

$$\displaystyle A^{-1} = \frac{1}{x}B$$

(Can someone tell me how to line up the = signs using LaTex?)

Last edited:

#### Subhotosh Khan

##### Super Moderator
Staff member
(Can someone tell me how to line up the = signs using LaTex?)
That I "believe" you can achieve by using spaces ( \ \ ).

Personally, I do not worry about it - unless I am preparing a manuscript to publish.

#### ausmathgenius420

##### New member
$$\displaystyle AB = xI$$
$$\displaystyle A^{-1} A B = A^{-1}. xI$$
$$\displaystyle IB = x A^{-1}I$$
$$\displaystyle B = x A^{-1}$$
$$\displaystyle \frac{1}{x}B = \frac{1}{x}.x A^{-1}$$

$$\displaystyle A^{-1} = \frac{1}{x}B$$

(Can someone tell me how to line up the = signs using LaTex?)
Thank you!

#### mmm4444bot

##### Super Moderator
Staff member
Can someone tell me how to line up the = signs using LaTex?
The align command is one of the many broken LaTeX functions at this forum (as seen in this post).