If AB = A and BA = B, where A and B are square matrices, then
AB = A ----- (i)
BA = B ------(ii)
From equation (ii)
B × (AB) = B
B2A= B
From equation (ii)
B2A = BA
B2 = B
From equation (i)
A × (BA) = A
A2B= A
From equation (i)
A2B = AB
A2 = A
Hence, A2 = A & B2 = B.
Option (A) is the correct answer.