If `A=[(a_(11),a_(12)),(a_(21),a_(22))]`, then minor of `a_(11) (i. e., M_(11))` is

Options

A. `a_(11)`
B. `a_(12)`
C. `a_(21)`
D. `a_(22)`

Answer

To find the minor of the element \( a_{11} \) in the matrix \( A = \begin{pmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{pmatrix} \), we follow these steps:

### Step 1: Identify the Element
The element \( a_{11} \) is located in the first row and first column of the matrix \( A \).

**Hint:** The minor of an element in a matrix is determined by removing the row and column of that element.

### Step 2: Remove the Row and Column
To find the minor \( M_{11} \), we need to remove the first row and the first column from the matrix \( A \). This leaves us with the remaining elements.

**Hint:** The remaining elements after removing the specified row and column will form a smaller matrix.

### Step 3: Form the Remaining Matrix
After removing the first row and first column, we are left with the element \( a_{22} \). Thus, the remaining matrix is simply \( \begin{pmatrix} a_{22} \end{pmatrix} \).

**Hint:** The minor is essentially the determinant of the smaller matrix formed after the removals.

### Step 4: Calculate the Determinant
The determinant of a \( 1 \times 1 \) matrix \( \begin{pmatrix} a_{22} \end{pmatrix} \) is simply the value of the single element itself, which is \( a_{22} \).

**Hint:** For a \( 1 \times 1 \) matrix, the determinant is the value of the element.

### Conclusion
Thus, the minor of \( a_{11} \) is given by:
\[ M_{11} = a_{22} \]

**Final Answer:** The minor of \( a_{11} \) is \( a_{22} \).