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Inverse of a Matrix
  • The inverse of a matrix is used in substitution for dividing. Matrices cannot be divided but they can be multiplied by an inverse.
  • Only square matrices have inverses.
  • The product of a matrix and its inverse will be an identity matrix of the same dimensions where all of the values are zero excluding a diagonal line of ones. It looks similar to this:

Let's Practice: Given below are two methods to find the inverse of a matrix O.

If , find  

Using Row Operations:
The following are the steps than can be taken to change a matrix into reduced row echelon form (rref):
  • Multiply a row by a scalar quantity.
  • Switching one row’s position with another.
  • Adding one multiple of a row to another multiple of a row.
Create an augmented matrix with the original matrix on the left and an identity matrix on the right. The dotted line is just there to distinguish between the different sides.

Using the Calculator:
  1. Press |ON|

  2. Press |2ND| and | | to access the matrix menu.

  3. Arrow to “EDIT” tab.

  4. Highlight [A] and press |ENTER|.

  5. Type “3”, |ENTER|, “3”, |ENTER|. This will set the dimensions of the matrix.

  6. You are now ready to insert the entries of matrix O from the previous example. Type each value starting from the top-left working right, pressing |ENTER| will tab to the next position.

  7. Press |2ND| |MODE| to return to the home screen.

  8. Press |2ND| and | | to access the matrix menu.

  9. [A] is highlighted, press |ENTER| to select it.

  10. Press | | for the inverse function.

  11. Press |ENTER| for it to calculate.

  12. Use the arrow keys to move right and see the other values in the matrix.

  13. To express answers in fractional form, press |MATH|.

  14. Press |ENTER|.

  15. Press |ENTER| for it to calculate.


What is your answer?

What is your answer?

T Rades

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