How to force GridView to generate square cells in Android

You can Override your linear layout

public class MyLinearLayout extends LinearLayout {
    public MyLinearLayout(Context context) {
        super(context);
    }

    public MyLinearLayout(Context context, AttributeSet attrs) {
        super(context, attrs);
    }

    public MyLinearLayout(Context context, AttributeSet attrs, int defStyleAttr) {
        super(context, attrs, defStyleAttr);
    }
    @Override
    public void onMeasure(int widthMeasureSpec, int heightMeasureSpec) {
        super.onMeasure(widthMeasureSpec, widthMeasureSpec); // This is the key that will make the height equivalent to its width
    }
}

then use it in the item_grid.xml

<?xml version="1.0" encoding="utf-8"?>
<com.example.MyLinearLayout xmlns:android="http://schemas.android.com/apk/res/android"
    android:orientation="vertical"
    android:layout_width="match_parent"
    android:layout_height="match_parent"
    android:background="@drawable/item_grid"

    android:layout_margin="2dp"
    android:padding="3dp"
    android:gravity="center">

    <TextView
        android:layout_width="wrap_content"
        android:layout_height="wrap_content"
        android:text="Category Name"
        android:textStyle="bold"
        android:textColor="@color/colorPrimary"
        android:id="@+id/tvCategoryName" />


</com.example.MyLinearLayout>

First, you're going to want to create a custom View class that you can use instead of the default LinearLayout you're using. Then you want to override the View's onMeasure call, and force it to be square:

public class GridViewItem extends ImageView {

    public GridViewItem(Context context) {
        super(context);
    }

    public GridViewItem(Context context, AttributeSet attrs) {
        super(context, attrs);
    }

    public GridViewItem(Context context, AttributeSet attrs, int defStyle) {
        super(context, attrs, defStyle);
    }

    @Override
    public void onMeasure(int widthMeasureSpec, int heightMeasureSpec) {
        super.onMeasure(widthMeasureSpec, widthMeasureSpec); // This is the key that will make the height equivalent to its width
    }
}

Then you can change your row_grid.xml file to:

<path.to.item.GridViewItem xmlns:android="http://schemas.android.com/apk/res/android"
    android:id="@+id/item_image"
    android:layout_width="match_parent"
    android:layout_height="match_parent"
    android:scaleType="centerCrop"
    android:src="@drawable/ic_launcher" >
</path.to.item.GridViewItem>

Just be sure to change "path.to.item" to the package where your GridViewItem.java class resides.

I also removed your LinearLayout parent since it wasn't doing anything for you there.

Edit:

Also changed scaleType from fitXY to centerCrop so that your image doesn't stretch itself and maintains its aspect ratio. And, as long as it's a square image, nothing should be cropped, regardless.