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$A=[a_{ij}]_{3\times3}$ and $B=[a_{ij}]_{3\times3}$ is

 $$\begin{align}&\lef

t( \begin{array}{ccc} a_{11} & a_{12}
& a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32}

& a_{33} \\ \end{array} \right)+ \left( \begin{array}{ccc} b_{11}
& b_{12} & b_{13} \\ b_{21}
&  b_{22} & b_{23} \\ b_{31}
&b_{32}
& b_{33} \\ \end{array} \right)= \left(\begin{array}{ccc}

a_{11}+b_{11}& a_{12}+b_{12}
& a_{13}+b_{13} \\ a_{21}+b_{21}
&a_{22}+b_{22}& a_{23}+b_{23}\\ a_{31}+b_{31}
&a_{32}+b_{32}
& a_{33}+b_{33}\\ \end{array}\right)\end{align}$$

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