Correct Answer: Option A

Explanation

S = \(\begin{pmatrix} -1 & 1 \\ 1 & -2 \end{pmatrix}\)
and ST = I  (Identity matrix).

This means  T  is the inverse of S 

Find the determinant of S  
\( \det(S)\) = (-1)(-2) - (1)(1) = 2 - 1 = 1

T = \(\frac{1}{\det(S)} \begin{pmatrix} -2 & -1 \\ -1 & -1 \end{pmatrix}\)
Since det = 1,  
T = \(\begin{pmatrix} -2 & -1 \\ -1 & -1 \end{pmatrix}\)
T = \(\begin{pmatrix} -2 & -1 \\ -1 & -1 \end{pmatrix}\)

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