How to Find the Inverse of a Matrix on the TI-84 Evo

To find the inverse of a matrix on the TI-84 Evo, type the matrix, then raise it to the power of negative one. The toggle key shows the answer as fractions.

This example finds the inverse of a 3 × 3 matrix:

A = 211544212

Type the matrix

  1. Press alpha, then zoom. That opens the matrix maker, a size picker with a ROW column and a COL column. The darkened numbers are the size it will build.
    The TI-84 Evo matrix maker, a size picker with ROW and COL columns and an OK button
  2. Press the up arrow until 3 is highlighted in the ROW column, then press enter. That sets 3 rows.
  3. Press the right arrow, then enter. The highlight moves across to the 3 in the COL column, and enter sets 3 columns.
    The size picker with 3 set in both the ROW and COL columns
  4. Press the down arrow until OK is highlighted, then press enter. An empty 3 × 3 matrix appears on the home screen.
    An empty 3 by 3 matrix of zeros on the TI-84 Evo home screen
  5. Type the entries, pressing the right arrow between them. The cursor works across the top row, then drops to the next one. Here that's 2, 1, 1 on the top row, 5, 4, 4 in the middle and 2, 1, 2 on the bottom.
    The 3 by 3 matrix filled in on the TI-84 Evo: 2, 1, 1 then 5, 4, 4 then 2, 1, 2

Find the inverse

  1. Press the right arrow once more. The cursor steps outside the brackets. Skip it and the −1 lands on the last entry instead of the whole matrix, which gives a wrong answer with no error.
  2. Press the power key, then the negative key, then 1. The TI-84 Evo has no x−1 key, so the inverse is typed as a power. The power key is the one marked x with a small box, just above x².
    TI-84 Evo keyboard with the power key highlighted, just above the x squared key
    The 3 by 3 matrix on the TI-84 Evo home screen with an exponent of negative 1
  3. Press enter. The inverse comes back in decimals, too wide for the screen. The small arrow at the right edge means a column is cut off.
    The inverse shown in decimals such as 1.333333333 and -0.3333333333, with its third column cut off at the right edge
  4. Press the toggle key, to the right of the 3 key. The inverse switches to fractions and fits on the screen: 4/3, −1/3 and 0 on the top row, −2/3, 2/3 and −1 in the middle, and −1, 0 and 1 on the bottom.
    TI-84 Evo keyboard with the fraction-decimal toggle key highlighted, to the right of the 3 key
    The TI-84 Evo showing the inverse as fractions: 4/3, -1/3, 0; -2/3, 2/3, -1; -1, 0, 1

If the matrix is stored as [A]

If you saved the matrix as [A] in the matrix editor (the matrix multiplication guide shows how), the inverse works the same way.

  1. Press 2nd, then vars. The blue MATRIX label above the vars key marks the matrix menu. Its NAMES tab lists each saved matrix with its size.
    The TI-84 Evo matrix menu on the NAMES tab with matrix A listed as 3x3
  2. With [A] highlighted, press enter. [A] lands on the home screen.
  3. Press the power key, the negative key, then 1, and press enter. The inverse comes back in decimals.
  4. Press the toggle key. The same fractions as before appear.
    The TI-84 Evo showing [A] to the negative 1 as a 3 by 3 matrix of fractions

Good to know

  • ERROR: SINGULAR MATRIX means there is no inverse. Some matrices don't have one; the numbers 1 through 9 in order are an example. Choose 1:Quit to get back to the home screen.
    The TI-84 Evo error screen reading ERROR: SINGULAR MATRIX, No inverse matrix exists, with Quit and Go to options
  • The matrix has to be square. A 2 × 3 matrix to the negative one gives ERROR: INVALID DIMENSION, and the help text ends with "Check inverse of square matrix only."
    The TI-84 Evo error screen reading ERROR: INVALID DIMENSION, ending with Check inverse of square matrix only
  • Press toggle again to go back to decimals.
  • The MATH menu's ▸Frac works too. Press math, then enter twice: the line reads Ans▸Frac and the same fractions come back.
  • The matrix maker remembers the last size. The next time you open it, the picker starts on the size you used before, so check both numbers before you choose OK.
  • Bigger matrices go through the matrix editor. The matrix maker stops at 6 rows and 6 columns; the editor takes up to 99 × 99.