#### ausmathgenius420

##### New member

- Joined
- Aug 5, 2021

- Messages
- 7

Hi,

My question is if you have 2 matrices A and B, such that:

[math]AB=24I[/math]How can I prove that;

[math]A^{-1}=\frac{1}{24}B[/math]

Intuitively it makes sense, however my textbook doesn't provide a proof for this which I'm curious about so hopefully someone can explain.

24I was just an example I chose. These equations can be generalised to

[math]AB=xI[/math]Thus

[math]A^{-1}=\frac{1}{x}B[/math]

My question is if you have 2 matrices A and B, such that:

[math]AB=24I[/math]How can I prove that;

[math]A^{-1}=\frac{1}{24}B[/math]

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

[math]AB=xI[/math]Thus

[math]A^{-1}=\frac{1}{x}B[/math]

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