
Nilpotent Matrix
Hi,
Is my working and answer to the following question correct?
Question: Show that matrix A is nilpotent and state the index of nilpotency k
$\displaystyle A = \begin {pmatrix}
2 & 1 \\
4 & 2
\end {pmatrix}$
Definition of Nilpotent: A matrix A is said to be nilpotent if $\displaystyle A^k=0$ for some positive integer k. The smallest k is called the index of nilpotency for A
$\displaystyle A^2 = \begin {pmatrix}
2 & 1 \\
4 & 2
\end {pmatrix}$$\displaystyle \begin {pmatrix}
2 & 1 \\
4 & 2
\end {pmatrix}$
$\displaystyle = \begin {pmatrix}
0 & 0 \\
0 & 0
\end {pmatrix}$
A is nilpotent, k=2


