Matrix product

The problem

Multiply two two-by-two matrices. Each output position is the dot product of one row from the left matrix and one column from the right matrix.

JavaScript

function mat2Mul(a, b) {
  return [
    [a[0][0]*b[0][0] + a[0][1]*b[1][0],
     a[0][0]*b[0][1] + a[0][1]*b[1][1]],
    [a[1][0]*b[0][0] + a[1][1]*b[1][0],
     a[1][0]*b[0][1] + a[1][1]*b[1][1]]
  ];
}
console.log(mat2Mul([[1,2],[3,4]], [[5,6],[7,8]]));

Python

def mat2_mul(a, b):
    return [
        [a[0][0]*b[0][0] + a[0][1]*b[1][0],
         a[0][0]*b[0][1] + a[0][1]*b[1][1]],
        [a[1][0]*b[0][0] + a[1][1]*b[1][0],
         a[1][0]*b[0][1] + a[1][1]*b[1][1]]
    ]
print(mat2_mul([[1,2],[3,4]], [[5,6],[7,8]]))

Julia

a = [1 2; 3 4]
b = [5 6; 7 8]
println(a * b)

RiX

Reading the RiX solution

These are tensor literals, not arrays of arrays. The 2x2 header records the shape and semicolons separate rows. RiX indexes from one, matching mathematical subscripts: left[1,2] means row one, column two.

Every output entry is a two-term dot product. The fixed-size implementation is repetitive by design; it exposes the invariant a general implementation must capture. For output (i, j), multiply left[i, k] by right[k, j] and add over valid k.

Exact arithmetic is preserved element by element. Replace one entry with 1 / 3 and the affected outputs remain rational. A general library would validate dimensions and express the repeated reduction once.