[devote]

используйте события onmouseenter, onmouseleave

<div id="la" style="width: 100px; height: 100px; background: #f00;">
    <a href="">test</a>
</div>
<script>
    document.getElementById('la').onmouseenter = function() {
        this.style.backgroundColor = '#0f0';
    }
    document.getElementById('la').onmouseleave = function() {
        this.style.backgroundColor = '#f00';
    }
</script>