Let A = \(\begin {bmatrix} a & b\\ c & d \end {bmatrix}\) i.e \(\begin{bmatrix} a & b\\c & d \end{bmatrix}\) \(\begin{bmatrix} 0 & 1\\2 & -1 \end{bmatrix}\) = \(\begin{bmatrix} 2 & -1\\1 & 0 \end{bmatrix}\) \(\implies \begin {bmatrix} a(0) + b(2) & a(1) + b(-1)\\ c(0) + d(2) & c(1) + d(-1)\end {bmatrix}\) = \(\begin {bmatrix} 2 & -1\\ 1 & 0 \end {bmatrix}\) \(\implies \begin {bmatrix} 2b & a - b\\2d & c - d\end {bmatrix}\) = \(\begin {bmatrix} 2 & -1\\ 1 & 0 \end {bmatrix}\) By comparing 2b = 2 a - b = -1 2d = 1 and c - d = 0 ∴ b = \(^2/_2\) = 1 a - b = -1 ⇒ a - 1 = -1 ∴ a = 0 ∴ d = \(^1/_2\) ⇒ c = d ∴ c = \(^1/_2\) ∴The matrice A = \(\begin {bmatrix} 0 & 1\\^1/_2 & ^1/_2 \end {bmatrix}\)