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