1. Problem statement: Multiply the matrices A and B and compute AB. A = $$\begin{pmatrix}1 & 2 \\ 3 & 4\end{pmatrix}$$. B = $$\begin{pmatrix}0 & 5 \\ 6 & 7\end{pmatrix}$$. 2. Formula and rules: For matrix multiplication, if A is m$\times$n and B is n$\times$p then AB is m$\times$p. The formula for each entry is $$ (AB)_{ij} = \sum_{k=1}^{n} A_{ik}B_{kj} $$. Dimension rule: the number of columns of A must equal the number of rows of B. 3. Intermediate work and computation: Compute each entry by taking the dot product of the appropriate row of A with the appropriate column of B. (AB)_{11} = 1\cdot0 + 2\cdot6 = 0 + 12 = 12. (AB)_{12} = 1\cdot5 + 2\cdot7 = 5 + 14 = 19. (AB)_{21} = 3\cdot0 + 4\cdot6 = 0 + 24 = 24. (AB)_{22} = 3\cdot5 + 4\cdot7 = 15 + 28 = 43. 4. Final answer: The product is $$AB = \begin{pmatrix}12 & 19 \\ 24 & 43\end{pmatrix}$$. 5. Explanation: Each entry of AB is the sum of pairwise products from a row of A and a column of B, which we computed step by step. Since both A and B are 2$\times$2 matrices, the result is also a 2$\times$2 matrix.