To determine the order of the determinant, we need to understand what the "order" of a determinant refers to. The order of a determinant is simply the number of rows or columns of the square matrix for which the determinant is being calculated.
Given matrix:
[tex]\[
\left|\begin{array}{ccc}
1 & 2 & 3 \\
5 & 3 & 2 \\
-3 & 1 & 2
\end{array}\right|
\][/tex]
We see that this matrix has 3 rows and 3 columns. This makes it a 3x3 matrix. Since the matrix is square (same number of rows and columns), the order of the determinant is 3.
So the correct answer is:
(ii) 3.
