Given: AAT=I=AT A where A is a square matrix and I is the identity matrix. Here, we have to find |A| ∵AAT=I ⇒|A.AT|=|I|=1 - - - - - - - -(∵Determinant of an identity matrix is always 1) As we know that, if A and B are two determinants of order n, then |A.B|=|A|.|B| ⇒|A.AT|=|A|.|AT|=1 As we know that, for any square matrix say A,|A|=|AT| ⇒|A|2=1 ⇒|A|=±1 Hence, option B is the correct answer.