Amit, Biraj and Chirag were given the task of creating a square matrux of order 2.
Below are the matrices created by them. A, B , C are the matrices created by Amit, Biraj and Chirag respectively.
`A=[(1,2),(-1,3)]B=[(4,0),(1,5)]C=[(2,0),(1,-2)]`
If a=4 and b=-2 based on the above information answer the following:
`(A^(T))^(T)` is equal to

Options

A. `[(1,2),(-1,3)]`
B. `[(2,1),(3,-1)]`
C. `[(1,-1),(2,3)]`
D. `[(2,3),(-1,1)]`

Answer

To find \((A^T)^T\), we need to follow these steps:

### Step 1: Identify the matrix A
The matrix \(A\) is given as:
\[ A = \begin{pmatrix} 1 & 2 \\ -1 & 3 \end{pmatrix} \]

### Step 2: Find the transpose of matrix A, denoted as \(A^T\)
To find the transpose of a matrix, we switch its rows with columns. Therefore, the transpose \(A^T\) is:
\[ A^T = \begin{pmatrix} 1 & -1 \\ 2 & 3 \end{pmatrix} \]

### Step 3: Find the transpose of \(A^T\), denoted as \((A^T)^T\)
Now, we need to find the transpose of \(A^T\). Again, we switch the rows with columns:
\[ (A^T)^T = \begin{pmatrix} 1 & -1 \\ 2 & 3 \end{pmatrix}^T = \begin{pmatrix} 1 & 2 \\ -1 & 3 \end{pmatrix} \]

### Conclusion
Thus, we find that:
\[ (A^T)^T = A = \begin{pmatrix} 1 & 2 \\ -1 & 3 \end{pmatrix} \]

### Final Answer
\((A^T)^T\) is equal to:
\[ \begin{pmatrix} 1 & 2 \\ -1 & 3 \end{pmatrix} \]

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