For nth order reaction, Rate =k[A]n
The unit of rate is M/s and the unit of [A] is M. Hence, the unit of rate constant k is M(1−n)/s
For the given reaction, the unit of rate constant is /s.
M(1−n)/s=/s
M(1−n)=M0
1−n=0
n=1
Hence, the reaction is of first order.