export function matrixInverse(matrix: number[][]): number[][] {
  const n = matrix.length;
  const identityMatrix = Array.from({ length: n }, (_, i) =>
    Array.from({ length: n }, (_, j) => (i === j ? 1 : 0))
  );
  const augmentedMatrix = matrix.map((row, i) => [
    ...row,
    ...identityMatrix[i]
  ]);

  for (let i = 0; i < n; i++) {
    let maxEl = Math.abs(augmentedMatrix[i][i]);
    let maxRow = i;
    for (let k = i + 1; k < n; k++) {
      if (Math.abs(augmentedMatrix[k][i]) > maxEl) {
        maxEl = Math.abs(augmentedMatrix[k][i]);
        maxRow = k;
      }
    }

    const temp = augmentedMatrix[maxRow];
    augmentedMatrix[maxRow] = augmentedMatrix[i];
    augmentedMatrix[i] = temp;

    for (let k = i + 1; k < n; k++) {
      const c = -augmentedMatrix[k][i] / augmentedMatrix[i][i];
      for (let j = i; j < 2 * n; j++) {
        if (i === j) {
          augmentedMatrix[k][j] = 0;
        } else {
          augmentedMatrix[k][j] += c * augmentedMatrix[i][j];
        }
      }
    }
  }

  for (let i = n - 1; i >= 0; i--) {
    for (let k = n; k < 2 * n; k++) {
      augmentedMatrix[i][k] /= augmentedMatrix[i][i];
    }
    augmentedMatrix[i][i] = 1;

    for (let rowModify = i - 1; rowModify >= 0; rowModify--) {
      const c = -augmentedMatrix[rowModify][i];
      for (let k = i; k < 2 * n; k++) {
        if (i === k) {
          augmentedMatrix[rowModify][k] = 0;
        } else {
          augmentedMatrix[rowModify][k] += c * augmentedMatrix[i][k];
        }
      }
    }
  }

  const inverseMatrix = augmentedMatrix.map((row) => row.slice(n));
  return inverseMatrix;
}