If matrix $A=[aij]_{2×2}$ where $aij=\left\{\begin{matrix} 1, i≠j\\0, i=j\end{matrix}\right.$,then $A^3$ is equal to :
Answer & explanation
Correct answer: option 4
$a_{ij}=1 \text{ for } i\ne j,\; a_{ij}=0 \text{ for } i=j.$
$A=\begin{bmatrix}0&1\\1&0\end{bmatrix}.$
$A^2=\begin{bmatrix}1&0\\0&1\end{bmatrix}=I.$
$A^3=A^2A=IA=A.$
$A^T=A.$
$A^3=A^T.$