1. Let's solve a simple example of matrix multiplication with two 2x2 matrices. 2. Suppose we have matrices: $$A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}, \quad B = \begin{bmatrix} 5 & 6 \\ 7 & 8 \end{bmatrix}$$ 3. The formula for matrix multiplication of two 2x2 matrices $A$ and $B$ is: $$C = A \times B = \begin{bmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{bmatrix} \times \begin{bmatrix} b_{11} & b_{12} \\ b_{21} & b_{22} \end{bmatrix} = \begin{bmatrix} a_{11}b_{11} + a_{12}b_{21} & a_{11}b_{12} + a_{12}b_{22} \\ a_{21}b_{11} + a_{22}b_{21} & a_{21}b_{12} + a_{22}b_{22} \end{bmatrix}$$ 4. Now, calculate each element of matrix $C$: - $c_{11} = 1 \times 5 + 2 \times 7 = 5 + 14 = 19$ - $c_{12} = 1 \times 6 + 2 \times 8 = 6 + 16 = 22$ - $c_{21} = 3 \times 5 + 4 \times 7 = 15 + 28 = 43$ - $c_{22} = 3 \times 6 + 4 \times 8 = 18 + 32 = 50$ 5. So the product matrix is: $$C = \begin{bmatrix} 19 & 22 \\ 43 & 50 \end{bmatrix}$$ This is how you multiply two 2x2 matrices step-by-step.