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==Examples==
* If the sum of two matrices is defined, that is, if they have the same order, then they are said to be ''conformable for addition''.
* Multiplication of two matrices is defined if and only if the number of columns of the left matrix is the same as the number of rows of the right matrix. That is, if {{math|'''A'''}} is an {{math|''m'' × ''n''}} matrix and {{math|'''B'''}} is an {{math|''s'' × ''p''}} matrix, then {{math|''n''}} needs to be equal to {{math|''s''}} for the matrix product {{math|'''AB'''}} to be defined. In this case, we say that {{math|'''A'''}} and {{math|'''B'''}} are ''conformable for multiplication'' (in that sequence).
* Since squaring a matrix involves multiplying it by itself ({{math|'''A'''<sup>'''2'''</sup> {{=}} '''AA'''}}) a matrix must be {{math|''m'' × ''m''}} (that is, it must be a [[square matrix]]) to be ''conformable for squaring''. Thus for example only a square matrix can be [[Idempotent matrix|idempotent]].
* Only a square matrix is ''conformable for [[matrix inversion]]''. However, the [[Moore-Penrose pseudoinverse]] and other [[generalized inverse]]s do not have this requirement.
* Only a square matrix is ''conformable for [[matrix exponentiation]]''.
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