If A = begin{bmatrix} 2 & 2 a & b end{bmatri | vedclass

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(A) Given $A = \begin{bmatrix} 2 & 2 \ a & b \end{bmatrix}$ and $A^2 = O$,where $O$ is the zero matrix $\begin{bmatrix} 0 & 0 \ 0 & 0 \end{bmatrix}$

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$(-2, -2)$

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(A) Given $A = \begin{bmatrix} 2 & 2 \ a & b \end{bmatrix}$ and $A^2 = O$,where $O$ is the zero matrix $\begin{bmatrix} 0 & 0 \ 0 & 0 \end{bmatrix}$.Calculate $A^2$:$A^2 = \begin{bmatrix} 2 & 2 \ a & b \end{bmatrix} \begin{bmatrix} 2 & 2 \ a & b \end{bmatrix} = \begin{bmatrix} 4 + 2a & 4 + 2b \ 2a + ab & 2a + b^2 \end{bmatrix}$.Equating $A^2$ to the zero matrix:$\begin{bmatrix} 4 + 2a & 4 + 2b \ 2a + ab & 2a + b^2 \end{bmatrix} = \begin{bmatrix} 0 & 0 \ 0 & 0 \end{bmatrix}$.From the first row:$4 + 2a = 0 \Rightarrow 2a = -4 \Rightarrow a = -2$.$4 + 2b = 0 \Rightarrow 2b = -4 \Rightarrow b = -2$.Check consistency with the second row:$2a + ab = 2(-2) + (-2)(-2) = -4 + 4 = 0$.$2a + b^2 = 2(-2) + (-2)^2 = -4 + 4 = 0$.Since all equations are satisfied,$(a, b) = (-2, -2)$.

If $A = \begin{bmatrix} 2 & 2 \\ a & b \end{bmatrix}$ and $A^2 = O$,then $(a, b) = $

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