In the determinant `|[0,1,-2],[-1, 0,3],[2,-3,0]|`, value of co-factor to its minor element of -3 is

Answer

To find the cofactor of the element -3 in the determinant

\[ \begin{vmatrix} 0 & 1 & -2 \\ -1 & 0 & 3 \\ 2 & -3 & 0 \end{vmatrix} \]

we will follow these steps:

### Step 1: Identify the position of the element -3
The element -3 is located in the third row and second column of the matrix. Therefore, we denote its position as \(a_{32}\).

### Step 2: Calculate the minor of the element -3
The minor \(M_{32}\) is calculated by removing the third row and the second column from the matrix. The remaining elements are:

\[ \begin{vmatrix} 0 & -2 \\ -1 & 3 \end{vmatrix} \]

### Step 3: Calculate the determinant of the minor
Now we compute the determinant of the 2x2 matrix:

\[ M_{32} = (0)(3) - (-2)(-1) = 0 - 2 = -2 \]

### Step 4: Calculate the cofactor
The cofactor \(C_{32}\) is given by the formula:

\[ C_{ij} = (-1)^{i+j} M_{ij} \]

For our case, \(i = 3\) and \(j = 2\):

\[ C_{32} = (-1)^{3+2} M_{32} = (-1)^{5} (-2) = -1 \times (-2) = 2 \]

### Final Answer
The value of the cofactor of the element -3 is:

\[ \boxed{2} \]