The inverse matrix is really hard to explain, but luckily it’s easy to show it’s effect. Open up blender, select default cube and press g z 1 LMB to move cube up 1 meter. Now shift+a->mesh->monkey to add monkey. G y 3 LMB to move monkey 3 meters on y axis. Press n to open n-panel and click item tab. The monkey is at 3 meters on the Y axis in reference to the world origin. Click monkey then shift+click cube and press Ctrl+p->object. As you can see, on the monkey nothing changed on it transforms. Now with both selected press alt+g. You’d expect both objects to goto world origin, but the monkey is at -1 on the z axis. This is because when the parent relationship was created the parent was at 1 z in reference to the world origin. To counter this you need to remove(inverse) that 1 z which is -1. That is what the inverse matric does. Now if you click the monkey and press alt+p->clear inverse the monkey will jump to the world origin. Hope that helps.
