The product of two matrices A and B will be possible if the number of columns of a Matrix A is equal to the number of rows of another Matrix B. A mathematical example of dot product of two matrices A & B is given below.

If

\(\displaystyle A=\left[ {\begin{array}{*{20}{c}} 1 & 2 \\ 3 & 4 \end{array}} \right]\)

and

\(\displaystyle B=\left[ {\begin{array}{*{20}{c}} 3 & 2 \\ 1 & 4 \end{array}} \right]\)

Then,

\(\displaystyle AB=\left[ {\begin{array}{*{20}{c}} 1 & 2 \\ 3 & 4 \end{array}} \right] \left[ {\begin{array}{*{20}{c}} 3 & 2 \\ 1 & 4 \end{array}} \right]\)

\(\displaystyle AB=\left[ {\begin{array}{*{20}{c}} {1\times 3+2\times 1} & {1\times 2+2\times 4} \\ {3\times 3+4\times 1} & {3\times 2+4\times 4} \end{array}} \right]=\left[ {\begin{array}{*{20}{c}} {3+2} & {2+8} \\ {9+4} & {6+16} \end{array}} \right]\)

\(\displaystyle AB=\left[ {\begin{array}{*{20}{c}} 5 & {10} \\ {13} & {22} \end{array}} \right]\)

Let’s start a practical example of dot product of two matrices A & B in python. First, we import the relevant libraries in Jupyter Notebook.

**Dot Product of two Matrices**

Let’s see another example of Dot product of two matrices C and D having different values.

If all the diagonal elements of a diagonal matrix are same, then it is called a Scalar Matrix. We can also take the dot product of two scalars which result will also a scalar, like this

Linear Algebra is mostly concerned with operations on vectors and matrices. Let’s take an example of dot product of one scalar and one vector…

It is clear from above snap that, the result obtained after taking dot product of a scalar and a vector is also a vector because a scalar value i.e. 2 is multiplied with each value of a vector i.e. 1, 2, 3 & 4 and we obtained a vector having values 2, 4, 6 & 8.

you might modify your example so that you multiple two matrices with different values so that it is clear how the elements are derived.