jee-advanced 2020 Q8

jee-advanced · India · paper1 3x3 Matrices Matrix Algebraic Properties and Abstract Reasoning

Let $M$ be a $3 \times 3$ invertible matrix with real entries and let $I$ denote the $3 \times 3$ identity matrix. If $M ^ { - 1 } = \operatorname { adj } ( \operatorname { adj } M )$, then which of the following statements is/are ALWAYS TRUE?
(A) $M = I$
(B) $\operatorname { det } M = 1$
(C) $M ^ { 2 } = I$
(D) $( \operatorname { adj } M ) ^ { 2 } = I$

Let $M$ be a $3 \times 3$ invertible matrix with real entries and let $I$ denote the $3 \times 3$ identity matrix. If $M ^ { - 1 } = \operatorname { adj } ( \operatorname { adj } M )$, then which of the following statements is/are ALWAYS TRUE?\\
(A) $M = I$\\
(B) $\operatorname { det } M = 1$\\
(C) $M ^ { 2 } = I$\\
(D) $( \operatorname { adj } M ) ^ { 2 } = I$

Paper Questions

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