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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def plot_probability_alive_matrix( model, max_frequency=None, max_recency=None, title="Probability Customer is Alive,\nby Frequency and Recency of a Customer", xlabel="Customer's Historical Frequency", ylabel="Customer's Recency", **kwargs ):
 """ Plot probability alive matrix as heatmap. Plot a figure of the probability a customer is alive based on their frequency and recency. Parameters model: lifetimes model A fitted lifetimes model. max_frequency: int, optional The maximum frequency to plot. Default is max observed frequency. max_recency: int, optional The maximum recency to plot. This also determines the age of the customer. Default to max observed age. title: str, optional Figure title xlabel: str, optional Figure xlabel ylabel: str, optional Figure ylabel kwargs Passed into the matplotlib.imshow command. Returns ------- axes: matplotlib.AxesSubplot """

    from matplotlib import pyplot as plt

    z = model.conditional_probability_alive_matrix(max_frequency, max_recency)

    interpolation = kwargs.pop("interpolation", "none")

    ax = plt.subplot(111)
    pcm = ax.imshow(z, interpolation=interpolation, **kwargs)
    plt.xlabel(xlabel)
    plt.ylabel(ylabel)
    plt.title(title)

    # turn matrix into square
    forceAspect(ax)

    # plot colorbar beside matrix
    plt.colorbar(pcm, ax=ax)

    return ax