Why is one way easier than the other for the same object?

Why is one way easier than the other for the same object?

As I exemplify below, one methodology/strategy can be easier than the
other for a given mathematical definition or object. Is there something
deeper and more expansive, beyond the examples below, which can illuminate
these questions?
$\Large{1.}$ Why is one way easier than the other, given that both
originate from the same object?
$\Large{2.}$ What should we do with this difference? Should the easy way
always be used?
$\Large{3.}$ How can we discover or divine which way is easier , without
trial and error? Sometimes books or lecturers do not discuss this.
œ Matrix multiplication: Row multiplication is regarded as easier than
column multiplication. I reference Introduction to Linear Algebra, 4th ed
by Gilbert Strang, which may help to unravel the difference:
It is a lot easier to see a combination of four vectors in $4D$ space,
than to visualize how four hyperplanes might possibly meet a point (Even
one hyperplane is hard enough...)
œ Determinant of a Matrix:
Laplace's Formula or Gaussian Elimination is probably easier than Cramer's
Rule or the Leibnitz Formula.
œ Product Rule instead of Quotient Rule:
$\cfrac{d}{dx} [f(x)g(x)]^{-1} $ with Product Rule can be easier than
$\cfrac{d}{dx} \left[\cfrac{f(x)}{g(x)}\right] $ with Quotient Rule.