Question

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

Every element of A is equal to it's co-factor

$A{A}^T=I$
$\Rightarrow A^{-1}=A^T$
$\Rightarrow A^T=adjA$ $(\because |A|=1)$
$\therefore$ Every element of $A$ is equal to it's co-factor.
Hence, option A.