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

Question

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

Quizplus · Accepted Answer

The Answer of A = $\left( \begin{array} { l l } 
a _ { 11 } & a _ { 12 } \
a _ { 21 } & a _ { 22 }
\end{array} \right)$ , B = $\left( \begin{array} { l l } 
b _ { 11 } & b _ { 12 } \
b _ { 21 } & b _ { 22 }
\end{array} \right)$ , and C = $\left( \begin{array} { l l l } 
c _ { 11 } & c _ { 12 } & c _ { 13 } \
c _ { 21 } & c _ { 22 } & c _ { 23 }
\end{array} \right)$ show that $( A + B ) ^ { \prime }$ = $A ^ { \prime }$ + $B ^ { \prime }$ and $( A C ) ^ { \prime }$ = $C ^ { \prime }$ $A ^ { \prime }$

A = (a11a12a21a22)\left( \begin{array} { l l } a _ { 11 } & a _ { 12 } \\a _ { 21 } & a _ { 22 }\end{array} \right)(a11​a21​​a12​a22​​)

A = $\left( \begin{array} { l l } a _ { 11 } & a _ { 12 } \\a _ { 21 } & a _ { 22 }\end{array} \right)$