Question

If $AA ^{ T }= I$ and $\text{det}( A )=1$, then -

• A. Every element of $A$ is equal to it's co-factor.
• B. Every element of $A$ and it's co-factor are additive inverse of each other.
• C. Every element of $A$ and it's co-factor are multiplicative inverse of each other.
• D. None of these

Answer 1

Answer: (A)

$A A^T=I \Rightarrow A^{-1}=A^T \Rightarrow A^T=\operatorname{adj} A$
$(\because|A|=1)$
$\therefore$ every element $=$ cofactor