Two-dimensional array in Swift

Define mutable array

// 2 dimensional array of arrays of Ints 
var arr = [[Int]]() 

OR:

// 2 dimensional array of arrays of Ints 
var arr: [[Int]] = [] 

OR if you need an array of predefined size (as mentioned by @0x7fffffff in comments):

// 2 dimensional array of arrays of Ints set to 0. Arrays size is 10x5
var arr = Array(count: 3, repeatedValue: Array(count: 2, repeatedValue: 0))

// ...and for Swift 3+:
var arr = Array(repeating: Array(repeating: 0, count: 2), count: 3)

Change element at position

arr[0][1] = 18

OR

let myVar = 18
arr[0][1] = myVar

Change sub array

arr[1] = [123, 456, 789] 

OR

arr[0] += 234

OR

arr[0] += [345, 678]

If you had 3×2 array of 0(zeros) before these changes, now you have:

[
  [0, 0, 234, 345, 678], // 5 elements!
  [123, 456, 789],
  [0, 0]
]

So be aware that sub arrays are mutable and you can redefine initial array that represented matrix.

Examine size/bounds before access

let a = 0
let b = 1

if arr.count > a && arr[a].count > b {
    println(arr[a][b])
}

Remarks: Same markup rules for 3 and N dimensional arrays.