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==Examples==
* In order to be conformable to addition or subtraction, matrices need to have the same dimensions. Thus ''A'', ''B'' and ''C'' all must have dimensions ''m'' × ''n'' in the equation
::<math>A + B = C</math>
:or
::<math>A - B = C</math>
:for some fixed ''m'' and ''n''.
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::<math>AB = C.</math>
:If ''A'' has dimensions ''m'' × ''n'', then ''B'' has to have dimensions ''n'' × ''p'' for some ''p'', so that ''C'' will have dimensions ''m'' × ''p''. That is, the number of columns in ''A'' must equal the number of rows in ''B'' for ''A'' and ''B'' to be conformable for multiplication in that sequence.
* Since squaring a matrix involves multiplying it by itself (<math>A^2=AA</math>) a matrix must be ''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]].
==See also==
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