import math

def matmul(mA:list[list[int]], mB:list[list[int]]) -> list[list[int]]:
    """
    Matrixmultiplication of matrizes with ints -> returns matrix as result
    :param mA:
    :param mB:
    :return:
    :raises ValueError: if Mismatch of Width first matrix and Height of second matrix
    """

    HeightA = len(mA)      ## zählt anzahl der listen in der äußeren Liste
    WidthA = len(mA[0])    ## zählt anzahl der elemente der nullten Liste
    HeightB = len(mB)
    WidthB = len(mB[0])

    if WidthA != HeightB:
        raise ValueError('Mismatch of Width of A and Height of B')

    result = [[0 for _ in range(WidthB)] for _ in range(HeightA)]


    for i in range(HeightA):
        for j in range(WidthB):
            for k in range(WidthA):
                result[i][j] += mA[i][k] * mB[k][j]


    return result


##=================================================================================
def transpose(matrix:list[list[int]]) -> list[list[int]]:
    """
    Transposes given matrix
    :param matrix:
    :return:
    :raises: ValueError if Inconsistent number of columns OR matrix is empty
    """
    if not matrix:
        raise ValueError('matrix is empty')

    height_old = len(matrix)
    width_old = len(matrix[0])

    for i in range(len(matrix) - 1):
        if len(matrix[i]) != len(matrix[i + 1]):
            raise ValueError('Inconsistent number of columns')

    result = [[0 for _ in range(height_old)] for _ in range(width_old)]
    height_new = len(result)
    width_new = len(result[0])


    for i in range(height_new):
        for j in range(width_new):
            result[i][j] = matrix[j][i]


    return result

##=================================================================================
def rot_2D(bogenmaß: float) -> list[list[float]]: ##auf Bogenmaß

    return [
        [math.cos(bogenmaß), -math.sin(bogenmaß)],
        [math.sin(bogenmaß), math.cos(bogenmaß)]
    ]
    ##rota matrix ist:  aus Aufgabe ggben
    ## cos  -sin
    ## sin  cos