Given the Following Matrices Show That $( \boldsymbol { A } + \boldsymbol { B } ) ^ { \prime } = \boldsymbol { A } ^ { \prime } + \boldsymbol { B } ^ { \prime }$

Essay

Given the following matrices $$\boldsymbol { A } = \left( \begin{array} { l l } a _ { 11 } & a _ { 12 } \\a _ { 21 } & a _ { 22 }\end{array} \right) , \boldsymbol { B } = \left( \begin{array} { l l } b _ { 11 } & b _ { 12 } \\b _ { 21 } & b _ { 22 }\end{array} \right) , \text { and } \boldsymbol { C } = \left( \begin{array} { l l l } c _ { 11 } & c _ { 12 } & c _ { 13 } \\c _ { 21 } & c _ { 22 } & c _ { 23 }\end{array} \right)$$
show that $( \boldsymbol { A } + \boldsymbol { B } ) ^ { \prime } = \boldsymbol { A } ^ { \prime } + \boldsymbol { B } ^ { \prime }$ and $( \boldsymbol { A } \boldsymbol { C } ) ^ { \prime } = \boldsymbol { C } ^ { \prime } \boldsymbol { A } ^ { \prime }$ .