ace test series

Question

 

how? please explain

Comments

Assume A = $\begin{bmatrix} 0&1 \\ 0 &0 \end{bmatrix}$

$A^{2}$ = $\begin{bmatrix} 0&1 \\ 0 &0 \end{bmatrix}$   X  $\begin{bmatrix}0&1 \\0 &0 \end{bmatrix}$ = $\begin{bmatrix}0&0 \\0 &0 \end{bmatrix}$

Rank($A^{2}$) = 0

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Thank you