^{-1}only when: A × A

^{-1}= A

^{-1}× A = I. In other words multiplying a matrix by its inverse equals the identity matrix.

Finding the inverse of a 2x2 matrix is simple; there is a formula for that. The bigger the matrix the bigger the problem. There are two methods to find the inverse of a matrix: using minors or using elementary row operations (also called the Gauss-Jordan method), both methods are equally tedious. We’ll be using the latter to find the inverse of matrices of order 3x3 or larger. For a review of matrix elementary row operations click here.

This is one of the things you really want Symbolab to do the magic.

Here’s an example of a 2x2 matrix - click here:

I neglected to mention that the formula is using the determinant, Symbolab does that too:

(Click here for the link to the matrix determinant calculator)

Here’s a more advanced example with a 3x3 matrix - click here:

Let’s zoom into the row operations:

…told you it’s no fun

Here’s the link to an example with a 4x4 matrix, not for the weakhearted - click here.

Cheers,

Michal