2. Solved Papers
  3. BCECE Engineering

BCECE Engineering BCECE Engineering Solved Paper-2006

  • question_answer
    If a square matrix A is such that \[A{{A}^{T}}=I={{A}^{T}}A,\] then \[|A|\] is equal to:

    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 spinner