Finding inverse of 3x3 order matrix

Id generally calc the determinant first as if its zero, the rest isnt that useful. But as you say, its zero.
Think about how matrix rows 1 and 2 and be linearly combined to get row 3. If they can be, the det is zero, its singular etc. So does there exist a and b such that
row3 = a*row1 + b*row2
Obviously, Id not be asking if a and b were not relatively simple/small.
Thinking about the geometry of the planes explains why this makes sense.

This is completely new to me. I spent the day yesterday learning it from scratch.
The steps to find the adjugate is what’s important for me.
If I don’t calculate that correctly, and find the deteriant to be greater than zero in another example, then I’m going to be wrong anyway lol.
If my approach is correct this way, I shall do another example where this is an inverse. Because, I need to verify if I can multiply correctly, too lol.

Not sure if its correct but you could enter it in wolfram to check (or another maths tool).
Instead of it being 9 at the end, you could make it 10 or 8 or .... just about any value but 9. If youre making up questions yourself though, why not google some exercises? That way theyve done the number crunching to ensure the answers are sensible (numbers not too big ....)

Yeah, I’m going to ask copilot lol. I’ll work through one with an inverse. Mmm, I tried Gauth but it uses A.I. I don’t how correct it is. I tested co-pilot and it had made errors in the past with some signs.

really dont use gauth. If you want a decent symplic solver Id just head to wolframalpha, but if you want 3*3 matrix inverse questions,
https://alevelmathsrevision.com/further-maths-categorised-exam-questions/
section 4 in https://www.sheffield.ac.uk/media/31962/download?attachment
or .... Just crack on with a bit of practice.

Nice links! As per the second one, asking to show the inverse is equal to that will help me determine if I am doing it right along the way.
When I first watched a video, there was nothing explaining about the checker board pattern and so that totally caught me off guard. Thanks for this