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Gram-positive bacteria are bacteria that have thick cell walls which yield positive results in the Gram staining test. Lipoteichoic acid is a major component of the cell wall of gram-positive bacteria.

All bacteria indicated in the question can be classified by the Gram staining test:

Actinomycetes are Gram-positive bacteria
The genus Arthrobacter includes Gram-positive bacteria
Escherichia coli (E. coli) is a Gram-negative bacterium
Staphylococcus spp. are Gram-positive bacteria
Bacillus spp are Gram-positive bacteria
Mycobacterium spp. are Gram-positive bacteria

Prokaryotes can be divided into two domains: Bacteria and Archaea.

Gram staining is a method used to classify bacteria, but this method IS NOT USED to stain Archaea.

In consequence, I would not use the Gram test to stain Archaebacteria because Archaebacteria aren't bacteria (Option A is correct).