#Javascript ES6, 44 bytes
One of the rare cases where I use every
a=>(c=a[0])?a.every(b=>b.length==c.length):a
f=
a=>(c=a[0])?a.every(b=>b.length==c.length):a
z.innerHTML = [
[],
[[1], [1], [2]],
[[1]],
[[1, 2, 3, 4]],
[[1, 2, 3, 4, 5], [2], [12, 314123]],
[[1, 2, 3, 4], [1]]
].map(m=>f(m)).join`<br>`<pre id=z>