Databinding, MaterialCardView should act like Radiogroup

I am trying to implement two MaterialCardViews that should act like a Radiogroup. So if I click one, the other should be unchecked. I am using viewModel, liveData and custom two-way data binding to save these values for later purpose (sending per email).

I had success writing the .xml and implementing the check logic, but I struggle implementing uncheck logic.

XML, short version for better visibility

<layout
    xmlns:app="http://schemas.android.com/apk/res-auto">

    <data>
        <variable
            name="vm"
            type="com.example.app.data.viewmodel.EmailViewModel" />
    </data>

        <com.google.android.material.card.MaterialCardView
            android:id="@+id/cardViewOne"
            android:checkable="true"
            android:clickable="true"
            android:focusable="true"
            <!-- Custom Two way databinding -->
            app:state_checked="@={vm.cardOptionOneChecked}"
        </com.google.android.material.card.MaterialCardView>


        <com.google.android.material.card.MaterialCardView
            android:id="@+id/cardViewTwo"
            android:checkable="true"
            android:clickable="true"
            android:focusable="true"
            <!-- Custom Two way databinding -->
            app:state_checked="@={vm.cardOptionTwoChecked}">

        </com.google.android.material.card.MaterialCardView>
</layout>

ViewModel

class EmailViewModel @ViewModelInject constructor(
    @Assisted private val savedStateHandle: SavedStateHandle
) : ViewModel() {

    // Variable for Id = cardViewOne
    val cardOptionOneChecked = MutableLiveData<Boolean>()
    
    // Variable for Id = cardViewTwo
    val cardOptionTwoChecked = MutableLiveData<Boolean>()
}

CardViewAdapter.kt

@BindingAdapter("state_checked")
fun setStateChecked(view: MaterialCardView, liveData: MutableLiveData<Boolean>) {
    if (view.isChecked != liveData.value) {
        liveData.value = view.isChecked
    }
}

@InverseBindingAdapter(attribute = "state_checked")
fun getStateChecked(view: MaterialCardView,): Boolean {
    return view.isChecked
}

// I don't know what logic belongs here to make it work! 
// Current approach just checks the current view and does nothing more. How can I save the last
// checked value?
@BindingAdapter("state_checkedAttrChanged")
fun setCheckedAttrListener(
    view: MaterialCardView,
    attrChange: InverseBindingListener,
) {
    view.apply {
        setOnClickListener { view.isChecked = true }
        setOnCheckedChangeListener { card, isChecked ->
            if (card.isChecked && card != view) {
                card.isChecked = false
            }
        }
        attrChange.onChange()
    }
}

I appreciate every help, thank you very much!

P.S: If there is a better and easier way to achieve this e.g. telling the viewModel from the view to save isChecked, please inform me. MaterialCardView has implemented "isChecked" by default but no logic.

Okay, I've solved the Problem:

First, Change Binding Adapter

I actually don't saw any way to use two-way data binding to achieve the above written case. Here is the new Binding Adapter

// View = Clicked MaterialCard, liveData = value in viewModel
@BindingAdapter("state_checked")
fun setStateChecked(view: MaterialCardView, liveData: MutableLiveData<Boolean>) {
    if (view.isChecked != liveData.value) {
        if (liveData.value != null) {
            view.isChecked = liveData.value!!
        }
    }
}

Second, Change XML Layout, because we don't use two-way data binding anymore

<layout
        xmlns:app="http://schemas.android.com/apk/res-auto">
    
        <data>
            <variable
                name="vm"
                type="com.example.app.data.viewmodel.EmailViewModel" />
        </data>
    
            <com.google.android.material.card.MaterialCardView
                android:id="@+id/cardViewOne"
                android:checkable="true"
                android:clickable="true"
                android:focusable="true"
                <!-- Deleted "=" -->
                app:state_checked="@{vm.cardOptionOneChecked}"
            </com.google.android.material.card.MaterialCardView>
    

            <com.google.android.material.card.MaterialCardView
                android:id="@+id/cardViewTwo"
                android:checkable="true"
                android:clickable="true"
                android:focusable="true"
                <!-- Deleted "=" -->
                app:state_checked="@{vm.cardOptionTwoChecked}">
    
            </com.google.android.material.card.MaterialCardView>
    </layout>

Third, Change viewmodel

class EmailViewModel @ViewModelInject constructor(
    @ApplicationContext context: Context,
    @Assisted private val savedStateHandle: SavedStateHandle
) : ViewModel() {

    val cardOptionOneChecked = MutableLiveData<Boolean>()
    
    val cardOptionTwoChecked = MutableLiveData<Boolean>()

    // Added
     fun firstCardClicked() {
        cardOneChecked.value = true
        cardTwoChecked.value = false
    }

    fun secondCardClicked() {
        cardOneChecked.value = false
        cardTwoChecked.value = true
    }
}

Fourth, add clickListener to XML or Fragment (here Fragment)

cardViewOne.setOnClickListener {
    viewModel.firstCardClicked()
}
cardViewTwo.setOnClickListener {
    viewModel.secondCardClicked()
}

If someone has any questions, just write it in the comments, I will help.