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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?
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?
Updated On: May 23, 2024
- $M=I$
- $\text{det} M=1$
- $M^{2}=I$
- $(\text{adj} M)^{2}=I$
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The Correct Option is B, C, D
Solution and Explanation
(B) $\text{det} M=1$
(C) $M^{2}=I$
(D) $(\text{adj} M)^{2}=I$
(C) $M^{2}=I$
(D) $(\text{adj} M)^{2}=I$
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