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

JEE Advanced 2020 Mathematics question

Let be a invertible matrix with real entries and let denote the identity matrix. If , then which of the following statements is/are ALWAYS TRUE?

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

For an invertible matrix, ; for this is . So . Taking determinants: (real entries).

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Question ID VK-033775