Question

Let $M$ be a $3 \times 3$ invertible matrix with real entries and let $I$ denote the $3 \times 3$ identity matrix. If $M^{-1}=\text{adj}(\text{adj} M)$, then which of the following statements is/are ALWAYS TRUE?

• A. $M=I$
• B. $\text{det} M=1$
• C. $M^{2}=I$
• D. $(\text{adj} M)^{2}=I$

Answer 1

Answer: (B), (C), (D)

$\text{det} M=1$

Answer 2

(B) $\text{det} M=1$
(C) $M^{2}=I$
(D) $(\text{adj} M)^{2}=I$