Consider a square matrix A or order 2 which has its elements as 0, 1, 2, 4. If the absolute value of `|A|` is least then, then absolute value of `|adj(adj(A))|` is equal to

Options

A. 0
B. 2
C. 1
D. 4

Answer

To solve the problem step by step, we need to find the absolute value of |adj(adj(A))| for a 2x2 matrix A with elements 0, 1, 2, and 4, such that the absolute value of the determinant |A| is minimized.

### Step 1: Identify Possible Matrices
The elements of matrix A can be arranged in a 2x2 matrix format. The possible matrices using the elements 0, 1, 2, and 4 are:
1. \( A = \begin{pmatrix} 0 & 2 \\ 1 & 4 \end{pmatrix} \)
2. \( A = \begin{pmatrix} 2 & 4 \\ 0 & 1 \end{pmatrix} \)
3. \( A = \begin{pmatrix} 0 & 1 \\ 2 & 4 \end{pmatrix} \)
4. \( A = \begin{pmatrix} 1 & 0 \\ 4 & 2 \end{pmatrix} \)
5. \( A = \begin{pmatrix} 1 & 2 \\ 0 & 4 \end{pmatrix} \)
6. \( A = \begin{pmatrix} 4 & 2 \\ 0 & 1 \end{pmatrix} \)