If `[{:(1,2,3):}] [{:(1,0,0),(0,1,0),(0,0,1):}][{:(1),(2),(3):}]=A,` then the order of matrix A is :

Options

A. `1 xx 3`
B. `3 xx 1 `
C. `3 xx 3`
D. `1 xx 1`

Answer

To determine the order of matrix A resulting from the multiplication of three matrices, we can follow these steps:

1. **Identify the order of the first matrix**: The first matrix is given as `[{:(1,2,3):}]`, which is a row matrix with 1 row and 3 columns. Therefore, its order is \(1 \times 3\).

2. **Identify the order of the second matrix**: The second matrix is `[{:(1,0,0),(0,1,0),(0,0,1):}]`, which is a square matrix with 3 rows and 3 columns. Therefore, its order is \(3 \times 3\).

3. **Multiply the first and second matrices**: When we multiply a matrix of order \(1 \times 3\) with a matrix of order \(3 \times 3\), the resulting matrix will have the order of the outer dimensions, which is \(1 \times 3\).

- Calculation:
- First matrix: \(1 \times 3\)
- Second matrix: \(3 \times 3\)
- Resulting matrix: \(1 \times 3\)

4. **Identify the order of the third matrix**: The third matrix is `[{:(1),(2),(3):}]`, which is a column matrix with 3 rows and 1 column. Therefore, its order is \(3 \times 1\).

5. **Multiply the resulting matrix from step 3 with the third matrix**: Now we multiply the resulting matrix of order \(1 \times 3\) with the third matrix of order \(3 \times 1\). The resulting matrix will have the order of the outer dimensions, which is \(1 \times 1\).

- Calculation:
- Resulting matrix from previous multiplication: \(1 \times 3\)
- Third matrix: \(3 \times 1\)
- Final resulting matrix (A): \(1 \times 1\)

6. **Conclusion**: The order of matrix A is \(1 \times 1\).

Thus, the final answer is that the order of matrix A is \(1 \times 1\).