Given A = (212312)\begin{pmatrix} 2 & 1 \\ 2 & 3 \\ 1 & 2 \end{pmatrix}221132 and B = (3242)\begin{pmatrix} 3 & 2 \\ 4 & 2 \end{pmatrix}(3422).
We can multiply these matrices since the number of colums in A = number of rows in B
AB = ((2⋅3)+(1⋅4)(2⋅2)+(1⋅2)(2⋅3)+(3⋅4)(2⋅2)+(3⋅2)(1⋅3)+(2⋅4)(1⋅2)+(2⋅2))\begin{pmatrix} (2\cdot 3)+(1\cdot 4) & (2\cdot 2)+(1\cdot 2) \\ (2\cdot 3)+(3\cdot 4) & (2\cdot 2)+(3\cdot 2) \\ (1\cdot 3)+(2\cdot 4) & (1\cdot 2)+(2\cdot 2) \end{pmatrix}(2⋅3)+(1⋅4)(2⋅3)+(3⋅4)(1⋅3)+(2⋅4)(2⋅2)+(1⋅2)(2⋅2)+(3⋅2)(1⋅2)+(2⋅2)
AB = ((6+4)(4+2)(6+12)(4+6)(3+8)(2+4))\begin{pmatrix} (6+4) & (4+2) \\ (6+12) & (4+6) \\ (3+8) & (2+4) \end{pmatrix}(6+4)(6+12)(3+8)(4+2)(4+6)(2+4)
= (1061810116)\begin{pmatrix} 10 & 6 \\ 18 & 10 \\ 11 & 6 \end{pmatrix}1018116106
