Some languages such as C# have native support for multidimensional arrays; Lua does not. You can create a multidimensional array in Lua by creating an array of arrays (really a table of tables). Doing so means you have to declare every element of an array to be a new row in the matrix or another array. You can achieve this as follows:

num_rows = 4
num_cols = 4

matrix = {} -- create new matrix
for i=1,num_rows do
  matrix[i] = {} -- create new row
  for j=1,num_cols do
    matrix[i][j] = i * j -- Assign value to row i, column j
  end
end

Once you have a matrix with several rows created, you can use double brackets to access elements within the matrix. The following piece of code shows this:

num_rows = 4
num_cols = 4

values = { 'A', 'B', 'C', 'D',
           'E', 'F', 'G', 'H',
           'I', 'J', 'K', 'L',
           'M', 'N', 'O', 'P'}
value = 1

matrix = {} -- create new matrix

for i=1,num_rows do
  matrix[i] = {} -- create new row

  for j=1,num_cols do
    -- current element: row i, column j
    -- assign current value to element
    matrix[i][j] = values[value] -- assign element to column

    value = value + 1 -- move to next letter
  end
end

-- print some elements
print (matrix[1][1])
print (matrix[2][4])
print (matrix[3][4])