Given,
A = ( 1 2 3 4 5 6 7 8 9 ) A = \begin{pmatrix}1&2&3\\ \:\:\:4&5&6\\ \:\:\:7&8&9\end{pmatrix} A = ⎝ ⎛ 1 4 7 2 5 8 3 6 9 ⎠ ⎞ B = ( 1 2 3 4 5 6 7 8 9 ) B = \begin{pmatrix}1&2&3\\ \:\:\:4&5&6\\ \:\:\:7&8&9\end{pmatrix} B = ⎝ ⎛ 1 4 7 2 5 8 3 6 9 ⎠ ⎞
Then,
A B = ( 1 2 3 4 5 6 7 8 9 ) ( 1 2 3 4 5 6 7 8 9 ) AB = \begin{pmatrix}1&2&3\\ \:\:\:4&5&6\\ \:\:\:7&8&9\end{pmatrix} \begin{pmatrix}1&2&3\\ \:\:\:4&5&6\\ \:\:\:7&8&9\end{pmatrix} A B = ⎝ ⎛ 1 4 7 2 5 8 3 6 9 ⎠ ⎞ ⎝ ⎛ 1 4 7 2 5 8 3 6 9 ⎠ ⎞
= ( 1 ⋅ 1 + 2 ⋅ 4 + 3 ⋅ 7 1 ⋅ 2 + 2 ⋅ 5 + 3 ⋅ 8 1 ⋅ 3 + 2 ⋅ 6 + 3 ⋅ 9 4 ⋅ 1 + 5 ⋅ 4 + 6 ⋅ 7 4 ⋅ 2 + 5 ⋅ 5 + 6 ⋅ 8 4 ⋅ 3 + 5 ⋅ 6 + 6 ⋅ 9 7 ⋅ 1 + 8 ⋅ 4 + 9 ⋅ 7 7 ⋅ 2 + 8 ⋅ 5 + 9 ⋅ 8 7 ⋅ 3 + 8 ⋅ 6 + 9 ⋅ 9 ) =\begin{pmatrix}1\cdot \:1+2\cdot \:4+3\cdot \:7&1\cdot \:2+2\cdot \:5+3\cdot \:8&1\cdot \:3+2\cdot \:6+3\cdot \:9\\ 4\cdot \:1+5\cdot \:4+6\cdot \:7&4\cdot \:2+5\cdot \:5+6\cdot \:8&4\cdot \:3+5\cdot \:6+6\cdot \:9\\ 7\cdot \:1+8\cdot \:4+9\cdot \:7&7\cdot \:2+8\cdot \:5+9\cdot \:8&7\cdot \:3+8\cdot \:6+9\cdot \:9\end{pmatrix} = ⎝ ⎛ 1 ⋅ 1 + 2 ⋅ 4 + 3 ⋅ 7 4 ⋅ 1 + 5 ⋅ 4 + 6 ⋅ 7 7 ⋅ 1 + 8 ⋅ 4 + 9 ⋅ 7 1 ⋅ 2 + 2 ⋅ 5 + 3 ⋅ 8 4 ⋅ 2 + 5 ⋅ 5 + 6 ⋅ 8 7 ⋅ 2 + 8 ⋅ 5 + 9 ⋅ 8 1 ⋅ 3 + 2 ⋅ 6 + 3 ⋅ 9 4 ⋅ 3 + 5 ⋅ 6 + 6 ⋅ 9 7 ⋅ 3 + 8 ⋅ 6 + 9 ⋅ 9 ⎠ ⎞
A B = ( 30 36 42 66 81 96 102 126 150 ) AB=\begin{pmatrix}30&36&42\\ 66&81&96\\ 102&126&150\end{pmatrix} A B = ⎝ ⎛ 30 66 102 36 81 126 42 96 150 ⎠ ⎞
#339914 on Dec 2023