Q44 / 160 · AP EAMCET 2018 (23 Apr Shift 2) · Mathematics

If $A=\left[\begin{array}{cc}0 & -1 \\ 1 & 0\end{array}\right]$, then the incorrect option among the following is

  • A
    $A^3-I=A(A-I)$
  • B
    $\left(A^3+I\right)=A\left(A^3-I\right)$
  • C
    $A^4-I=A^2+I$
  • Correct answer
    D
    $A^2+I=A\left(A^2-l\right)$

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.

Hence, the correct answer is option: 'D'.

Relevant Questions