By taking any advanced math course or even scanning through this website, you quickly learn how powerful a graphing calculator can be. A more “theoretical” course like linear algebra is no exception. In fact, once you know how to do something like finding an inverse matrix by hand, the calculator can free you up from that calculation and let you focus on the big picture.

Remember, not every matrix has an inverse. The matrix picked below is *invertible*, meaning it does in fact have an inverse. We will talk about what happens when it isn’t invertible a little later on. Here is the matrix we will use for our example:

\( \left[ \begin{array}{cccc} 8 & 2 & 1 & 6 \\ 8 & 4 & 1 & 1 \\ 0 & 2 & 6 & 4 \\ 15 & 8 & 9 & 20 \end{array} \right]\)

**Note: for a video of these steps, scroll down.**

### Step 1: Get to the Matrix Editing Menu

This is a much more involved step than it sounds like! If you have a TI 83, there is simply a button that says “MATRIX”. This is the button you will click to get into the edit menu. If you have a TI84, you will have to press [2ND] and [\(x^{-1}\)]. This will take you into the menu you see below. Move your cursor to “EDIT” at the top.

### Step 2: Enter the Matrix

First, you must tell the calculator how large your matrix is. Just remember to keep it in order of “rows” and “columns”. For example, our example matrix has 4 rows and 4 columns, so I type 4 [ENTER] 4 [ENTER].

### Step 3: Select the Matrix Under the NAMES Menu

After you have quit by clicking [2ND] and [MODE], go back into the matrix menu by clicking [2ND] and [\(x^{-1}\)] (or just the matrix button if you have a TI83). This time, select A from the NAMES menu by clicking [ENTER].

### Step 4: Press the Inverse Key [\(x^{-1}\)] and Press Enter

The easiest step yet! All you need to do now, is tell the calculator what to do with matrix A. Since we want to find an inverse, that is the button we will use.

### Step 5: (OPTIONAL) Convert Everything to Fractions

While the inverse is on the screen, if you press [MATH] , 1: Frac, and then ENTER, you will convert everything in the matrix to fractions. Then, as before, you can click the right arrow key to see the whole thing.

Oh yeah – so what happens if your matrix is singular (or NOT invertible)? **In other words, what happens if your matrix doesn’t have an inverse?**

## Video walkthrough

The following video will walk you through the steps above.

## Additional reading

You may also find it useful to be able to row reduce a matrix using your calculator or even multiply matrices.

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