Step 2: Understand that the determinant is a value that can tell us about the matrix's properties.
Step 3: Check if the rows of the matrix are linearly dependent. This means that one row can be made by adding or multiplying the other rows.
Step 4: Notice that each row is a multiple of the others. For example, the second row (2, 2, 2) is 2 times the first row (1, 1, 1), and the third row (3, 3, 3) is 3 times the first row.
Step 5: Since the rows are linearly dependent, the determinant of the matrix is 0.
