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

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.