# Thread: Simple linear question !

1. ## Simple linear question !

Good day to all,

While reading my professor's notes on matrix inverses he asks if we can tell without computing why the following equation (attached image) is not true
with the X meaning multiplication.

I feel embarrassed asking the question but I cannot seem to see why. At first I thought it was because the maximum rank of the first matrix is 3 as well as the second's while the resulting matrix rank is 4. But I am not sure if this is the avenue I should be exploring. What I am seeking is some guidance and not necessarily the answer. Any help would be greatly appreciated.

Kindest regards

2. Hello! I'm sorry but I see no equation.

3. Thanks Bruno J. for the remarked. I have since attached the image that contains the equation.

4. The reason you give is correct. If you want to look at it in another way, consider the linear transformations which these matrices represent; what does the dimension theorem tell you?

5. Any inverse matrix must be square matrix ($\displaystyle n\times n$)

Demo matrix is $\displaystyle R^{4\times 3}$ and $\displaystyle R^{3\times 4}$ , so it's not invertible matrix

6. Thank you both for your prompt attention to the matter. I will look into the dimension theorem as well.