Matrix Multiplication Calculator (Solver)
Formula
\( \begin{bmatrix} a_{11}&a_{12}&a_{13}&a_{14}&a_{15}\\a_{21}&a_{22}&a_{23}&a_{24}&a_{25}\\a_{31}&a_{32}&a_{33}&a_{34}&a_{35}\\a_{41}&a_{42}&a_{43}&a_{44}&a_{45}\\a_{51}&a_{52}&a_{53}&a_{54}&a_{55} \end{bmatrix}\times\begin{bmatrix} b_{11}&b_{12}&b_{13}&b_{14}&b_{15}\\b_{21}&b_{22}&b_{23}&b_{24}&b_{25}\\b_{31}&b_{32}&b_{33}&b_{34}&b_{35}\\b_{41}&b_{42}&b_{43}&b_{44}&b_{45}\\b_{51}&b_{52}&b_{53}&b_{54}&b_{55} \end{bmatrix} \)=
=\(\begin{bmatrix} a_{11} \times b_{11}+a_{12} \times b_{21}+a_{13} \times b_{31}+a_{14} \times b_{41}+a_{15} \times b_{51}&a_{11} \times b_{12}+a_{12} \times b_{22}+a_{13} \times b_{32}+a_{14} \times b_{42}+a_{15} \times b_{52}&a_{11} \times b_{13}+a_{12} \times b_{23}+a_{13} \times b_{33}+a_{14} \times b_{43}+a_{15} \times b_{53}&a_{11} \times b_{14}+a_{12} \times b_{24}+a_{13} \times b_{34}+a_{14} \times b_{44}+a_{15} \times b_{54}&a_{11} \times b_{15}+a_{12} \times b_{25}+a_{13} \times b_{35}+a_{14} \times b_{45}+a_{15} \times b_{55}\\a_{21} \times b_{11}+a_{22} \times b_{21}+a_{23} \times b_{31}+a_{24} \times b_{41}+a_{25} \times b_{51}&a_{21} \times b_{12}+a_{22} \times b_{22}+a_{23} \times b_{32}+a_{24} \times b_{42}+a_{25} \times b_{52}&a_{21} \times b_{13}+a_{22} \times b_{23}+a_{23} \times b_{33}+a_{24} \times b_{43}+a_{25} \times b_{53}&a_{21} \times b_{14}+a_{22} \times b_{24}+a_{23} \times b_{34}+a_{24} \times b_{44}+a_{25} \times b_{54}&a_{21} \times b_{15}+a_{22} \times b_{25}+a_{23} \times b_{35}+a_{24} \times b_{45}+a_{25} \times b_{55}\\a_{31} \times b_{11}+a_{32} \times b_{21}+a_{33} \times b_{31}+a_{34} \times b_{41}+a_{35} \times b_{51}&a_{31} \times b_{12}+a_{32} \times b_{22}+a_{33} \times b_{32}+a_{34} \times b_{42}+a_{35} \times b_{52}&a_{31} \times b_{13}+a_{32} \times b_{23}+a_{33} \times b_{33}+a_{34} \times b_{43}+a_{35} \times b_{53}&a_{31} \times b_{14}+a_{32} \times b_{24}+a_{33} \times b_{34}+a_{34} \times b_{44}+a_{35} \times b_{54}&a_{31} \times b_{15}+a_{32} \times b_{25}+a_{33} \times b_{35}+a_{34} \times b_{45}+a_{35} \times b_{55}\\a_{41} \times b_{11}+a_{42} \times b_{21}+a_{43} \times b_{31}+a_{44} \times b_{41}+a_{45} \times b_{51}&a_{41} \times b_{12}+a_{42} \times b_{22}+a_{43} \times b_{32}+a_{44} \times b_{42}+a_{45} \times b_{52}&a_{41} \times b_{13}+a_{42} \times b_{23}+a_{43} \times b_{33}+a_{44} \times b_{43}+a_{45} \times b_{53}&a_{41} \times b_{14}+a_{42} \times b_{24}+a_{43} \times b_{34}+a_{44} \times b_{44}+a_{45} \times b_{54}&a_{41} \times b_{15}+a_{42} \times b_{25}+a_{43} \times b_{35}+a_{44} \times b_{45}+a_{45} \times b_{55}\\a_{51} \times b_{11}+a_{52} \times b_{21}+a_{53} \times b_{31}+a_{54} \times b_{41}+a_{55} \times b_{51}&a_{51} \times b_{12}+a_{52} \times b_{22}+a_{53} \times b_{32}+a_{54} \times b_{42}+a_{55} \times b_{52}&a_{51} \times b_{13}+a_{52} \times b_{23}+a_{53} \times b_{33}+a_{54} \times b_{43}+a_{55} \times b_{53}&a_{51} \times b_{14}+a_{52} \times b_{24}+a_{53} \times b_{34}+a_{54} \times b_{44}+a_{55} \times b_{54}&a_{51} \times b_{15}+a_{52} \times b_{25}+a_{53} \times b_{35}+a_{54} \times b_{45}+a_{55} \times b_{55} \end{bmatrix}\)
=\(\begin{bmatrix} a_{11} \times b_{11}+a_{12} \times b_{21}+a_{13} \times b_{31}+a_{14} \times b_{41}+a_{15} \times b_{51}&a_{11} \times b_{12}+a_{12} \times b_{22}+a_{13} \times b_{32}+a_{14} \times b_{42}+a_{15} \times b_{52}&a_{11} \times b_{13}+a_{12} \times b_{23}+a_{13} \times b_{33}+a_{14} \times b_{43}+a_{15} \times b_{53}&a_{11} \times b_{14}+a_{12} \times b_{24}+a_{13} \times b_{34}+a_{14} \times b_{44}+a_{15} \times b_{54}&a_{11} \times b_{15}+a_{12} \times b_{25}+a_{13} \times b_{35}+a_{14} \times b_{45}+a_{15} \times b_{55}\\a_{21} \times b_{11}+a_{22} \times b_{21}+a_{23} \times b_{31}+a_{24} \times b_{41}+a_{25} \times b_{51}&a_{21} \times b_{12}+a_{22} \times b_{22}+a_{23} \times b_{32}+a_{24} \times b_{42}+a_{25} \times b_{52}&a_{21} \times b_{13}+a_{22} \times b_{23}+a_{23} \times b_{33}+a_{24} \times b_{43}+a_{25} \times b_{53}&a_{21} \times b_{14}+a_{22} \times b_{24}+a_{23} \times b_{34}+a_{24} \times b_{44}+a_{25} \times b_{54}&a_{21} \times b_{15}+a_{22} \times b_{25}+a_{23} \times b_{35}+a_{24} \times b_{45}+a_{25} \times b_{55}\\a_{31} \times b_{11}+a_{32} \times b_{21}+a_{33} \times b_{31}+a_{34} \times b_{41}+a_{35} \times b_{51}&a_{31} \times b_{12}+a_{32} \times b_{22}+a_{33} \times b_{32}+a_{34} \times b_{42}+a_{35} \times b_{52}&a_{31} \times b_{13}+a_{32} \times b_{23}+a_{33} \times b_{33}+a_{34} \times b_{43}+a_{35} \times b_{53}&a_{31} \times b_{14}+a_{32} \times b_{24}+a_{33} \times b_{34}+a_{34} \times b_{44}+a_{35} \times b_{54}&a_{31} \times b_{15}+a_{32} \times b_{25}+a_{33} \times b_{35}+a_{34} \times b_{45}+a_{35} \times b_{55}\\a_{41} \times b_{11}+a_{42} \times b_{21}+a_{43} \times b_{31}+a_{44} \times b_{41}+a_{45} \times b_{51}&a_{41} \times b_{12}+a_{42} \times b_{22}+a_{43} \times b_{32}+a_{44} \times b_{42}+a_{45} \times b_{52}&a_{41} \times b_{13}+a_{42} \times b_{23}+a_{43} \times b_{33}+a_{44} \times b_{43}+a_{45} \times b_{53}&a_{41} \times b_{14}+a_{42} \times b_{24}+a_{43} \times b_{34}+a_{44} \times b_{44}+a_{45} \times b_{54}&a_{41} \times b_{15}+a_{42} \times b_{25}+a_{43} \times b_{35}+a_{44} \times b_{45}+a_{45} \times b_{55}\\a_{51} \times b_{11}+a_{52} \times b_{21}+a_{53} \times b_{31}+a_{54} \times b_{41}+a_{55} \times b_{51}&a_{51} \times b_{12}+a_{52} \times b_{22}+a_{53} \times b_{32}+a_{54} \times b_{42}+a_{55} \times b_{52}&a_{51} \times b_{13}+a_{52} \times b_{23}+a_{53} \times b_{33}+a_{54} \times b_{43}+a_{55} \times b_{53}&a_{51} \times b_{14}+a_{52} \times b_{24}+a_{53} \times b_{34}+a_{54} \times b_{44}+a_{55} \times b_{54}&a_{51} \times b_{15}+a_{52} \times b_{25}+a_{53} \times b_{35}+a_{54} \times b_{45}+a_{55} \times b_{55} \end{bmatrix}\)
This on-line calculator will help you calculate the product of two matrices.