# How can i compute inverse of 3-dimensional matrix?

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Rajeev Prajapati on 22 May 2015
Edited: Walter Roberson on 22 May 2015
If
a11=[0.1 0.4 0.5 0.6];
a12=[0.5 0.04 0.045 0.0006];
a13 = [0.0055 0.4 0.0445 0.10006];
a21 = [0.155 0.1044 0.045 0.1006];
a22 = [0.55 0.104 0.2045 0.06];
a23 = [0.55 0.0044 0.45 0.006];
a31= [0.155 0.1044 0.045 0.1006];
a32=[0.1 0.9 0.005 0.006];
a33=[0.001 0.002 0.002 0.105];
Then, how can i compute inverse of matrix A=[a11,a12,a13;a21,a22,a23;a31,a32,a33]?

John D'Errico on 22 May 2015
The inverse of a 3-d matrix has no definition in mathematics that I know of. So in order to do what you want, you first need to define that operation. Then you need to write code for that purpose.

Youssef Khmou on 22 May 2015
There is misunderstanding between the question and the provided example, according the question, Jhon's answer is correct, three dimensional matrices are out of scope, but the example you gave is a 3 by 12 matrix, generally for non square matrix, the inverse is generalized inverse pinv(A).