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True or False: $(A^3)^{-1}=(A^{-1})^3$,where A is a square matrix and $|\;A\;|\neq 0$

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1 Answer

Toolbox:
  • $A^{-1}=\frac{1}{|A|}(adj A)$
  • If a non singular matrix of order n,then $(A^n)^{-1}=(A^{-1})^n$
By the information in the toolbox,
$(A^n)^{-1}=(A^{-1})^n$
Here n=3.
Therefore $(A^3)^{-1}=(A^{-1})^3$
Hence the given statement is True.
answered Mar 27, 2013 by sreemathi.v
 

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