How do you easily create empty matrices javascript?

There is something about Array.fill I need to mention.

If you just use below method to create a 3x3 matrix.

Array(3).fill(Array(3).fill(0));

You will find that the values in the matrix is a reference.

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Optimized solution (prevent passing by reference):

If you want to pass by value rather than reference, you can leverage Array.map to create it.

Array(3).fill(null).map(() => Array(3).fill(0));

Array.fill

Consider using fill:

Array(9).fill().map(()=>Array(9).fill())

The idea here is that fill() will fill out the items with undefined, which is enough to get map to work on them.

You could also fill directly:

Array(9).fill(Array(9))

(important note: Array(9).fill(Array(9)) will fill each row of the array with the same array, so changing one row will change the other rows).

Alternatives to Array(9).fill() include

Array(...Array(9))
[].push(...Array(9))
[].concat(Array(9))
Array.from(Array(9))

We can rewrite the solution a bit more semantically as:

function array9() { return Array(9).fill(); }
array9().map(array9)

or

function array(n) { return Array(n).fill(); }
array(9).map(() => array(9))

Array.from provides us with an optional second mapping argument, so we have the alternative of writing

Array.from(Array(9), () => Array.from(Array(9));

or, if you prefer

function array9(map) { return Array.from(Array(9), map); }
array9(array9);

For verbose description and examples, see Mozilla's Docs on Array.prototype.fill() here.
and for Array.from(), here.

Note that neither Array.prototype.fill() nor Array.from() has support in Internet Explorer. A polyfill for IE is available at the above MDN links.

Partitioning

partition(Array(81), 9)

if you have a partition utility handy. Here's a quick recursive one:

function partition(a, n) {
  return a.length ? [a.splice(0, n)].concat(partition(a, n)) : [];
}  

Looping

We can loop a bit more efficiently with

var a = [], b;
while (a.push(b = []) < 9) while (b.push(null) < 9);

Taking advantage of the fact that push returns the new array length.

var matrix = [];
for(var i=0; i<9; i++) {
    matrix[i] = new Array(9);
}

... or:

var matrix = [];
for(var i=0; i<9; i++) {
    matrix[i] = [];
    for(var j=0; j<9; j++) {
        matrix[i][j] = undefined;
    }
}