  It is shown that Sarnak's M\"{o}bius orthogonality conjecture is fulfilled
for the compact metric dynamical systems for which every invariant measure has
singular spectra. This is accomplished by first establishing a special case of
Chowla conjecture which gives a correlation between the M\"{o}bius function and
its square. Then a computation of W. Veech, followed by an argument using the
notion of `affinity between measures', (or the so-called `Hellinger method'),
completes the proof. We further present an unpublished theorem of Veech which
is closely related to our main result. This theorem asserts, if for any
probability measure in the closure of the Cesaro averages of the Dirac measure
on the shift of the M\"{o}bius function, the first projection is in the
orthocomplement of its Pinsker algebra then Sarnak M\"{o}bius disjointness
conjecture holds. Among other consequences, we obtain a simple proof of
Matom{\"a}ki-Radziwi{\l}l-Tao's theorem and Matom{\"a}ki-Radziwi{\l}l's theorem
on the correlations of order two of the Liouville function.
