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Answer:  $C = \begin{bmatrix} -3 &4 &-1 \\ -3& 0 &-1 \end{bmatrix}$

Hint: Zero matrix is $\begin{bmatrix} 0 &0 \\ 0& 0 \end{bmatrix}$

Add A and B matrices. Then, find C.

Given: $A =\begin{bmatrix} 1 &-3 &2 \\ 2 & 0 &2 \end{bmatrix} , B =\begin{bmatrix} 2 &-1 & -1\\ 1& 0 & -1 \end{bmatrix} , A + B + C = 0$

Here, we have to compute C.

Solution:

$A + B + C =\begin{bmatrix} 0 &0 &0 \\ 0& 0 & 0 \end{bmatrix}$

$\begin{bmatrix} 1 & -3 &2 \\ 2 &0 &2 \end{bmatrix} +\begin{bmatrix} 2 & -1&-1 \\ 1& 0 & -1 \end{bmatrix} + C = \begin{bmatrix} 0 &0 &0 \\ 0& 0& 0 \end{bmatrix}$

$\begin{bmatrix} 3 & -4 &1\\ 3 &0 &1 \end{bmatrix} + C = \begin{bmatrix} 0 &0 &0 \\ 0& 0& 0 \end{bmatrix}$

$C = \begin{bmatrix} 0 &0 &0 \\ 0& 0& 0 \end{bmatrix}-\begin{bmatrix} 3 & -4 &1\\ 3 &0 &1 \end{bmatrix}$

$C = \begin{bmatrix} -3 &4 &-1 \\ -3& 0 &-1 \end{bmatrix}$

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