Question

How do I find the inverse of a matrix?

Answer 1

A matrix only has an inverse if it is a square matrix (like 2x2 or 3x3...) and its determinant is not equal to 0.

First, to find a determinant by hand, we can look at a 2x2:

In my calculator, you see the abbreviation of determinant is "det".
The calculator knows to expect a square matrix inside the parentheses, otherwise this command would not be possible.

For a 2x2, you can see the product of the first diagonal subtracted by the product of the second diagonal. Simple.

Then, you take the reciprocal of that answer (-34), and multiply that as a scalar multiple on a new matrix where you switch the positions of the 3 and -2 (first diagonal), and change signs on the second diagonal (7 and 4). In this example, some of the fractions were reduced.

A 3x3 matrix is not as easy, and I would usually suggest using a calculator like i did here:

I hope this was helpful. Ask another question if you are interested in more about inverse matrices!