A matrix is
a rectangular array of numbers. The size and shape of the array
is given by the number of rows and columns it contains, called its
order. So a matrix with 3 rows and 2 columns is described as having
order 3 by 2. This is not the same as a matrix
of order 2 by 3, which has 2 rows and 3 columns.

is a 4 x 3 matrix. The element a_{2,3} or A[2,3]
is 7. In terms of the mathematical definition given above,
this matrix is a function **A : {1, 2, 3, 4} x {1, 2, 3} **^{__}> R