permutation matrix? $\sigma=(132)(45)$ be a permutation, we construct the matrix $A$ such that its $i'$th collumn is the $\sigma(i)'$th colllumn of $I_5$.
so the matrix which I got is ${A}=\left[\begin{array}{*{20}{c}}
{0}&{1}&{0}&0&0&0\\
{0}&{0}&{1}&0&0&0\\
{1}&{0}&{0}&0&0&0\\
{0}&{0}&{0}&0&0&1\\
{0}&{0}&{0}&0&1&0\\
\end{array}\right]$
now I need to say which of the followng is correct?


*

*$A^3=I$

*$A^5=I$

*$A^6=I$

*$A^2=I$
without doing product how to say the answer? what is the underlying theory here?
thanks

your permutation has two cycles one of length $3$ and the other of length $2.$ the permutation is of the order $6$ which is the least common multiple of the orders. i expect $A^6 = I.$
