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Linear-Algebra · Matrix-Inverse

Inverse of [[0,-1],[1,0]]

\left[\begin{matrix}0 & -1\\1 & 0\end{matrix}\right]

Step by step

  1. \det A = 1

    A matrix is invertible only when its determinant is non-zero.

  2. A^{-1} = \frac{1}{\det A}\begin{pmatrix} d & -b \\ -c & a \end{pmatrix} = \frac{1}{1}\left[\begin{matrix}0 & 1\\-1 & 0\end{matrix}\right]

    For 2×2: swap the diagonal, negate the off-diagonal, divide by the determinant.

  3. A^{-1} = \left[\begin{matrix}0 & 1\\-1 & 0\end{matrix}\right]

Reveal the answer
A^{-1} = \left[\begin{matrix}0 & 1\\-1 & 0\end{matrix}\right]