Matrix Multiplication Calculator

Intro: Computes the matrix product AB (when dimensions match) and shows the dot-product calculation for each entry.

Worked example

• Compute AB where $A = [[1, 2],[3, 4]]$ and $B = [[5, 6],[7, 8]]$.



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• We have $A=\begin{pmatrix}1 & 2\\3 & 4\end{pmatrix}$ and $B=\begin{pmatrix}5 & 6\\7 & 8\end{pmatrix}$.



• Matrix A is 2×2 and matrix B is 2×2, so the product AB is defined and will also be 2×2.



• The entry $(AB)_{11}$ is the dot product of row 1 of A with column 1 of B: $1\cdot5 + 2\cdot7 = 5+14=19$.



• The entry $(AB)_{12}$ is row 1 of A with column 2 of B: $1\cdot6 + 2\cdot8 = 6+16=22$.



• The entry $(AB)_{21}$ is row 2 of A with column 1 of B: $3\cdot5 + 4\cdot7 = 15+28=43$.



• The entry $(AB)_{22}$ is row 2 of A with column 2 of B: $3\cdot6 + 4\cdot8 = 18+32=50$.



• So $AB = \begin{pmatrix}19 & 22\\43 & 50\end{pmatrix}$.



• Answer: $\boxed{AB = \begin{pmatrix}19 & 22\\43 & 50\end{pmatrix}.}$

Why choose MathGPT?

• Get clear, step-by-step solutions that explain the “why,” not just the answer.
• See the rules used at each step (power, product, quotient, chain, and more).
• Optional animated walk-throughs to make tricky ideas click faster.
• Clean LaTeX rendering for notes, homework, and study guides.

How this calculator works

• Type or paste your function (LaTeX like \sin, \ln works too).
• Press Generate a practice question button to generate the derivative and the full reasoning.
• Review each step to understand which rule was applied and why.
• Practice with similar problems to lock in the method.

Related

• Matrix Inverse
• RREF (Row-Reduced Echelon Form)