Finding an inverse matrix on the TI 83/84 calculators

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1 An example

Image of matrix inverse TI83

On this page we will show how to use a TI83/84 calculator to find the invese of a matrix. The matrix we will use in this example is the following.


A =  \left[ 
    \begin{array}{rrr} 
      2& 3&-4\\ 
      1&-2& 0\\ 
      3& 0& 1 
    \end{array} 
  \right]


Already know how to enter a matrix? then jump to step 5.

2 The steps on a TI83 or TI84

Images of TI83 showing the matrix key

Step 1)

The first step is to find the MATRIX menu (press 2ND then the x–1 key). Click on the image to see a larger view of the calculator keys if you have trouble finding the MATRIX key.

Press the MATRIX key.

Images of TI83 showing matrix table

Step 2)

When you press MATRIX, you will get a menu across the top:

NAMES MATH EDIT

Use the arrow keys to highlight the EDIT menu item. To edit matrix A (the one we usually use), just press ENTER.

Images of TI83 showing the matrix edit window

Step 3)

The first thing we must do is indicate the size. Enter the number of rows first, press enter, then the number of columns, then press enter again. (In our example these are 3 and 3.)


Image of TI83

Step 4)

Now add the entries one at a time, followed by ENTER. You may also use the arrow keys to move around the menu.

Notice that as you add entries in larger matrices, any entries that are off the screen slide over onto the screen for editing.

Image of TI83
Image of TI83
Step 5)

Now we must enter [A]-1 on the calculator. We find [A] by going to the Matrix menu (as in step 1) and pressing ENTER with NAMES and A highlighted (left). This will put [A] on the main screen.

Now just hit the x-1 key and again press ENTER (right). (Warning: you must use the x-1 key, not "^-1".)

Image of TI83

Step 6)

Success, but with a problem. This example has an ugly answer.

Note that we can use the arrow keys to slide over and see the other three columns of this matrix that are off the screen.

If you get an error, remember that only square matrices with non-zero determinant have an inverse.

Image of TI83

Step 7)

Often we can clean up answers by going to the math menu (image on right) and selecting the convert to fraction item (the first, so just press the MATH button, then press ENTER, then ENTER again to convert the previous answer (our matrix) into fractions).

Image of TI83

Step 8)

Success! We now can see that the inverse of our matrix is the following.


\left[ 
    \begin{array}{rrr} 
      \frac{2}{31} & \frac{3}{31} & \frac{8}{31}\\[4pt] 
      \frac{1}{31} &-\frac{14}{31}& \frac{4}{31}\\[4pt] 
      -\frac{6}{31}&-\frac{9}{31} & \frac{7}{31} 
    \end{array} 
  \right]
= \frac{1}{31} \left[ 
    \begin{array}{rrr} 
      2& 3& 8\\ 
      1&-14& 4\\ 
      -6& -9& 7 
    \end{array} 
  \right]


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