1. The problem is to understand and interpret the matrix $A$ given as: $$A=\begin{bmatrix}1 & 2 & 3 \\ 0 & 1 & 4 \\ 5 & 6 & 0\end{bmatrix}$$ 2. A matrix is a rectangular array of numbers arranged in rows and columns. Here, $A$ is a $3 \times 3$ matrix, meaning it has 3 rows and 3 columns. 3. Each element of the matrix is denoted by $a_{ij}$ where $i$ is the row number and $j$ is the column number. For example, $a_{11} = 1$, $a_{23} = 4$, and $a_{32} = 6$. 4. This matrix can be used in various algebraic operations such as addition, multiplication, finding determinants, inverses, and solving systems of linear equations. 5. To summarize, the matrix $A$ is: $$\begin{bmatrix}1 & 2 & 3 \\ 0 & 1 & 4 \\ 5 & 6 & 0\end{bmatrix}$$ which is a standard $3 \times 3$ matrix with the elements as shown. This completes the interpretation of the matrix $A$.