mat.rb

class Matrix
  attr_reader :elements

  def initialize(elements)
    @elements = elements
  end

  def dimensions
    { rows: @elements.first.count, cols: @elements.count }
  end

  def can_be_multiplied_with(other_matrix)
    dimensions[:rows] == other_matrix.dimensions[:cols]
  end

  def *(other_matrix)
    if can_be_multiplied_with other_matrix
      new_elements = (0...dimensions[:cols]).map do |k|
        (0...dimensions[:rows]).map do |i|
          (0...dimensions[:rows]).map do |j|

            @elements[k][j] * other_matrix.elements[j][i]

          end.reduce(:+)
        end
      end

      Matrix.new(new_elements)
    else
      throw "Matrix dimensions do not match up; Cannot multiply."
    end
  end

  # Ignore, just necessary to do `m1 * m2`
  def coerce(other)
    return self, other
  end
end