Given `[(4,2),(-1,1)]`M = 6 I, where M is a matrix and I is the unit matrix or order `2xx2`.
(i) State the order of matrix M.

Answer

To determine the order of matrix \( M \) given the equation \( [(4,2),(-1,1)]M = 6I \), where \( I \) is the unit matrix of order \( 2 \times 2 \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Matrices**:
We have a matrix \( A = \begin{pmatrix} 4 & 2 \\ -1 & 1 \end{pmatrix} \) and we know that \( I \) is the identity matrix of order \( 2 \times 2 \), which is \( I = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} \).

2. **Understand the Matrix Multiplication**:
The equation \( A \cdot M = 6I \) implies that the product of matrix \( A \) and matrix \( M \) results in a matrix that is \( 6 \) times the identity matrix.

3. **Determine the Order of Matrix \( A \)**:
Matrix \( A \) is a \( 2 \times 2 \) matrix since it has 2 rows and 2 columns.

4. **Matrix Multiplication Rules**:
For the multiplication of two matrices to be defined, the number of columns in the first matrix must equal the number of rows in the second matrix. Therefore, if \( A \) is \( 2 \times 2 \) and \( M \) is \( r \times c \), we must have:
\[ \text{Number of columns in } A = \text{Number of rows in } M \implies 2 = r \]

5. **Determine the Order of Matrix \( M \)**:
Since \( A \) is \( 2 \times 2 \) and the resulting matrix \( 6I \) is also \( 2 \times 2 \), the number of columns in \( M \) must also be 2 (to match the resulting matrix). Thus, we have:
\[ \text{Number of columns in } M = 2 \implies c = 2 \]

6. **Conclusion**:
Therefore, matrix \( M \) must be of order \( 2 \times 2 \).

### Final Answer:
The order of matrix \( M \) is \( 2 \times 2 \).