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We use the identity matrix to calculate a the inverse of a square matrix. In order to be invertible, a matrix must be square. By finding the square matrix inverse, we can find the solution of a system of linear equations. A square matrix inverse, when multiplied on the left or right by the original matrix gives us the identity matrix.

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APA style
What is the Inverse of a Square Matrix?. (2013, March 2). In ClassBrain Math Tutorials. Retrieved 09:24, September 22, 2017, from http://www.classbrainmath.com/inverse-of-a-square-matrix/
MLA style
Cynthia Kirkeby, “What is the Inverse of a Square Matrix?.” ClassBrain Math Tutorials. 2 March 2013, 10:09 UTC. . 22 Sep 2017 <http://www.classbrainmath.com/inverse-of-a-square-matrix/>.
MHRA style
Cynthia Kirkeby, 'What is the Inverse of a Square Matrix?', ClassBrain Math Tutorials, 2 March 2013, 10:09 UTC, <http://www.classbrainmath.com/inverse-of-a-square-matrix/> [accessed 22 September 2017]
The Chicago Manual of Style
Cynthia Kirkeby, “What is the Inverse of a Square Matrix?.” ClassBrain Math Tutorials, http://www.classbrainmath.com/inverse-of-a-square-matrix/ [accessed September 22, 2017].
CBE/CSE style
Cynthia Kirkeby, What is the Inverse of a Square Matrix? [Internet]. ClassBrain Math Tutorials; 2013 March 2, 10:09 UTC [cited 2017 Sep 22]. Available from: http://www.classbrainmath.com/inverse-of-a-square-matrix/.
Bluebook style
What is the Inverse of a Square Matrix?, http://www.classbrainmath.com/inverse-of-a-square-matrix/ (last visited Sep. 22, 2017).
AMA style
Cynthia Kirkeby, What is the Inverse of a Square Matrix?. ClassBrain Math Tutorials. March 2, 2013, 10:09 UTC. Available at: http://www.classbrainmath.com/inverse-of-a-square-matrix/. Accessed September 22, 2017.