SparkNotes Shopping Cart  |     |  Checkout
Brought to you by Barnes and Noble
  Home : Math & Science : Math Study Guides : Algebra II : Matrices : The Inverse of a Matrix
Matrices
  
 
The Inverse of a Matrix
The Inverse of a Matrix
The multiplicative inverse of a real number is the number that yields 1 (the identity) when multiplied by the original number. is the multiplicative inverse of a, because a× = 1.
Most matrices also have a multiplicative inverse. In other words, for the majority of matrices A, there exists a matrix A-1 such that AA-1 = I and A-1A = I. For example, the inverse of

A =    

is

A-1 =    

because

=    


and

= .    

To find the inverse of an m×m matrix, write the m×m matrix on the left, and the m×m identity matrix to the right:

   


Then, row reduce to convert the matrix to reduced row-echelon form--that is, to get an m×m identity matrix on the left. The new m×m matrix on the right is the multiplicative inverse of the original matrix. In other words, the new m×m matrix times the original m×m matrix yields the identity matrix.

Example: Find the multiplicative inverse of:

.    


  1.    

  2.    

  3.    

  4.    

  5.    

  6.    

Thus, the multiplicative inverse of

   

is

.    

Help | Feedback | Make a request | Report an error | Send to a friend
 
You'll flip over our Pre-Algebra Study Cards—writing out flashcards is now a thing of the past.
More...
 
Study right for the SAT II Chemistry test with the experts at SparkNotes.
More...
 
 
Go to top