A) 0
B) \[\pm \,1\]
C) \[\pm \,2\]
D) none of these
Correct Answer: B
Solution :
The Given, A is a square matrix and \[A{{A}^{T}}=I={{A}^{T}}A\] \[\Rightarrow \] \[|A{{A}^{T}}|=|I|=|{{A}^{T}}A|\] \[\Rightarrow \] \[|A||{{A}^{T}}|=1=|{{A}^{T}}||A|\] \[\Rightarrow \] \[|A{{|}^{2}}=1\] \[(\because \,|{{A}^{T}}|=|A|)\] \[\Rightarrow \] \[|A|=\pm 1.\]You need to login to perform this action.
You will be redirected in
3 sec