Multiplication of Matrices
A = [latex]\begin{pmatrix} a & e\\b & f\\c & g\\d & h\end{pmatrix}[/latex]
Let the matrix:
B = [latex]\begin{pmatrix} j & k & l\\m & n & o\end{pmatrix}[/latex]
Therefore:A × B = [latex]\begin{pmatrix} aj+em & ak+en & al+eo\\bj+bm & bk+bn & bl+bo\\cj+cm & ck+cn & cl+co\\dj+dm & dk+dn & dl+do\end{pmatrix}[/latex]
Example
Let the matrix:A = [latex]\begin{pmatrix} 3 & -3\\5 & 1\\2 & -2\\6 & 9\end{pmatrix}[/latex]
Let the matrix:B = [latex]\begin{pmatrix} -5 & 7 & -6\\0 & -2 & 8\end{pmatrix}[/latex]
Therefore:A × B = [latex]\begin{pmatrix} 3 × -5 + -3 × 0 & 3 × 7+ -3 × -2 & 3 × -6 + -3 × 8\\5 × -5 + 1 × 0 & 5 × 7 + 1 × -2 & 5 × -6 + 1 × 8 \\2 × -5 + -2 × 0 & 2 × 7 + -2 × -2 & 2 × -6 + -2 × 8 \\6 × -5 + 9 × 0 & 6 × 7 + 9 × -2 & 6 × -6 + 9 × 8 \end{pmatrix} = \begin{pmatrix} -15 & 27 & -42 \\-25 & 33 & -22 \\-10 & 18 & -28 \\-30 & 24 & 36 \end{pmatrix}[/latex]