Matrix is the rectangular array of elements or numbers. Matrix multiplication multiplies the given two matrices.
If A and B are two matrices of any order the matrix multiplication is possible iff m $\times$ p = p $\times$ n and resultant matrix will be of the order m $\times n where m, n and p are the order of the matrices. Matrix Multiplication Calculator calculates the matrix multiplication of matrices of order 2$\times$2 as well as 3$\times$3. Let us see an example for 2$\times$2 Matrix multiplication to understand the steps properly: Consider two Matrices A and B Where Observe the problem from top row of first matrix and first column of second matrix. Then follow these steps. Step 1: Multiply each number from top row of first matrix with the number in the first column of second matrix and their product to get (a$\times$p) + (b$\times$r) = ap + br Step 2: Similarly multiply each number from top row with second column of second matrix and add the product to get (a$\times$q) + (b$\times$s) = aq + bs Step 3: In the same way multiply each number of second row of first with first column of second matrix and add to get (c$\times$p) + (d$\times$r) = cp + dr Step 4: Finally multiply each number of second row with second column of second matrix and add to get (c$\times$q) + (d$\times$s) = cq + ds The matrix multiplication is ## Matrix Multiplication Problems Below are given some problems based on matrix multiplication for both 2$\times$2 and 3$\times$3 matrix. ### Solved Examples Question 1: Find the value of AB if A =$\begin{bmatrix} 1 &2 \\ 3 &4 \end{bmatrix} and B = \begin{bmatrix} 2 & 4\\ 6 & 8 \end{bmatrix}$Solution: A =$\begin{bmatrix} 1 &2 \\ 3 &4 \end{bmatrix} and B = \begin{bmatrix} 2 & 4\\ 6 & 8 \end{bmatrix}\\
A \times B = \begin{bmatrix} 1 \times 2 + 2 \times 6 & 1 \times 4 + 2 \times 8 \\ 3 \times 2 + 4 \times 6 & 3 \times 4 + 4 \times8 \end{bmatrix}\\
= \begin{bmatrix} 14 & 20\\ 30 & 44 \end{bmatrix}$Question 2: Find the matrix multiplication A =$\begin{bmatrix}
1 & 0 & 1\\
0 & 0 & 1\\
0 & 2 & 1
\end{bmatrix} and\ B =  \begin{bmatrix}
1 & 2 & 1\\
0 & 3 & 4\\
1 & 1 & 0
\end{bmatrix}$. Solution: A =$\begin{bmatrix} 1 & 0 & 1\\ 0 & 0 & 1\\ 0 & 2 & 1 \end{bmatrix} and\ B = \begin{bmatrix} 1 & 2 & 1\\ 0 & 3 & 4\\ 1 & 1 & 0 \end{bmatrix}\\
A \times B = \begin{bmatrix} 1\times1+0 \times0 + 1 \times1 & 1 \times2 + 0\times3 + 1\times1 &1\times1+0\times4+1\times0 \\ 0\times1+0\times0+1\times1 &0\times2+0\times3+1\times1 &0\times1+0\times4+1\times0 \\ 0\times1+2\times0+1\times1 &0\times2+2\times3+1\times1 &0\times1+2\times4+1\times0 \end{bmatrix}\\
= \begin{bmatrix} 2 & 3 &1 \\ 1 & 1 &0 \\ 1 & 7 &8 \end{bmatrix}\$