Compute `[(a,0),(a,0)][(0,0),(0,0)]`.

Answer

To compute the multiplication of the matrices \(\begin{pmatrix} a & 0 \\ a & 0 \end{pmatrix}\) and \(\begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix}\), we will follow the standard procedure for matrix multiplication.

### Step-by-Step Solution:

1. **Identify the matrices**:
- Let \( A = \begin{pmatrix} a & 0 \\ a & 0 \end{pmatrix} \)
- Let \( B = \begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix} \)

2. **Check the dimensions**:
- Matrix \( A \) is of size \( 2 \times 2 \) (2 rows and 2 columns).
- Matrix \( B \) is also of size \( 2 \times 2 \).
- Since the number of columns in \( A \) is equal to the number of rows in \( B \), we can multiply these matrices.

3. **Set up the resultant matrix**:
- The resultant matrix \( C \) will also be of size \( 2 \times 2 \).
- Let \( C = \begin{pmatrix} c_{11} & c_{12} \\ c_{21} & c_{22} \end{pmatrix} \)

4. **Calculate each element of the resultant matrix**:
- **Element \( c_{11} \)**:
\[ c_{11} = (a \cdot 0) + (0 \cdot 0) = 0 + 0 = 0 \]
- **Element \( c_{12} \)**:
\[ c_{12} = (a \cdot 0) + (0 \cdot 0) = 0 + 0 = 0 \]
- **Element \( c_{21} \)**:
\[ c_{21} = (a \cdot 0) + (0 \cdot 0) = 0 + 0 = 0 \]
- **Element \( c_{22} \)**:
\[ c_{22} = (a \cdot 0) + (0 \cdot 0) = 0 + 0 = 0 \]

5. **Construct the resultant matrix**:
- Thus, the resultant matrix \( C \) is:
\[ C = \begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix} \]

### Final Result:
The result of the multiplication \(\begin{pmatrix} a & 0 \\ a & 0 \end{pmatrix} \begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix}\) is:
\[ \begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix} \]