1. ## matrix problem

$
\begin{bmatrix}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 1 & 0 & -1 & 0 \\ -2 & 1 & 0 & -1\end{bmatrix}
$

That's A and I have to compute A^2010
I'm given a hint to first compute A^2

2. If you calculate $A^2$ you get the following matrix:
$\begin{bmatrix}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1\end{bmatrix}$
As you can see its the $I$ matrix and therefore
$A^3=I*A => A$
So you always get either A matrix or the I matrix depending on your square.
If its an even square you get the I matrix otherwise A matrix.
A^2010 you do the math.

3. Originally Posted by wicked
If you calculate $A^2$ you get the following matrix:
$\begin{bmatrix}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1\end{bmatrix}$
As you can see its the $I$ matrix and therefore
$A^3=I*A => A$
So you always get either A matrix or the I matrix depending on your square.
If its an even square you get the I matrix otherwise A matrix.
A^2010 you do the math.
thank you so much ! You're a life saver