If A is a square matrix satisfying A'A=I, write the value \left | A \right |.

 

 

 

 

 
 
 
 
 

Answers (1)

Given : 

\left | A'A \right |=\left | I \right |

            \Rightarrow \left | A' \right |\left | A \right |=\left | I \right |

            \Rightarrow \left | A \right |\left | A \right |= I\left [\because \left | A' \right | =\left | A \right | \right ]

            \Rightarrow \left | A \right |^{2}=1\left [ \because \left | I \right |=1 \right ]

            \Rightarrow \left | A \right |=\pm 1

 

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