If $A=\left[\begin{array}{cc}0 & -1 \\ 1 & 0\end{array}\right]$, then the incorrect option among the…
If $A=\left[\begin{array}{cc}0 & -1 \\ 1 & 0\end{array}\right]$, then the incorrect option among the following is
$A^3-I=A(A-I)$
$\left(A^3+I\right)=A\left(A^3-I\right)$
$A^4-I=A^2+I$
$A^2+I=A\left(A^2-l\right)$
Solution
For the given matrix $A=\left[\begin{array}{cc}0 & -1 \\ 1 & 0\end{array}\right]$ the characteristics equation is $A^2+I=0$, so the $A^3=-A$ and $A^4=I$.
Now, if we analyse, the option $A^2+I=A\left(A^2-I\right)$ is incorrect.