Question

If $A{A}^T=I$ 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)

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