Write the order of the product matrix :
`[(1),(2),(3)]["2 3 4"]`

Answer

To find the order of the product matrix given by the multiplication of two matrices, we will follow these steps:

### Step 1: Identify the order of the first matrix
The first matrix is given as `[(1), (2), (3)]`, which is a column matrix with 3 rows and 1 column. Therefore, the order of this matrix is:
\[ \text{Order of first matrix} = 3 \times 1 \]

### Step 2: Identify the order of the second matrix
The second matrix is given as `["2 3 4"]`, which is a row matrix with 1 row and 3 columns. Therefore, the order of this matrix is:
\[ \text{Order of second matrix} = 1 \times 3 \]

### Step 3: Check if the matrices can be multiplied
To multiply two matrices, the number of columns in the first matrix must equal the number of rows in the second matrix. Here:
- The first matrix has 1 column.
- The second matrix has 1 row.

Since both are equal (1 = 1), we can multiply these matrices.

### Step 4: Determine the order of the product matrix
The order of the product matrix is given by the number of rows from the first matrix and the number of columns from the second matrix. Therefore, the order of the product matrix will be:
\[ \text{Order of product matrix} = \text{(Number of rows of first matrix)} \times \text{(Number of columns of second matrix)} \]
Substituting the values:
\[ \text{Order of product matrix} = 3 \times 3 \]

### Final Answer
Thus, the order of the product matrix is:
\[ \text{Order of product matrix} = 3 \times 3 \]

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