An Array of Challenges #1: Alternating Arrays

Jelly, 4 bytes

ḣ2ṁ⁼

Try it online!

How it works

ḣ2ṁ⁼  Main link. Argument: A (array)

ḣ2    Head 2; truncate A after its second element. If A has two or less elements,
      this returns A itself.
  ṁ   Mold; cyclically repeat the elements of the previous result to create an
      array that has the same shape/length as A.
   ⁼  Test the result for equality with A.

brainfuck, 34 bytes

,>,>+>,
[
  [<+<<->>>-]
  +<[-<<]
  >[>]
  ,
]
<.

Takes the array as byte values in a string, and outputs \x00 for false and \x01 for true.

Try it online.

This maintains the structure

a b 1 c

on the tape, where c is the current character, b is the previous character, and a is the previous previous character, as long as the array is alternating. If a mismatch is found, the pointer is moved to the left such that a, b, and the 1 flag all become zero, and this situation will continue until all the input is consumed.

R, 24 23 bytes

all((a=scan())==a[1:2])

Reads a vector into STDIN, takes the first two elements of that vector, and checks equality. If the lengths of a[1:2] and a don't match, R will loop through a[1:2] to match the length of a. It will give a warning about doing so, but it will work.

Surprisingly this even works for empty input, not sure why, but I'll roll with it.

Saved 1 byte thanks to @MickyT