Let M be a 3×3 invertible matrix with real entries and let I denote the 3×3 identity matrix. If M−1=adj(adjM) , then which of the following statements is/are ALWAYS TRUE?
A
M=I
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B
detM=1
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C
M2=I
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D
(adjM)2=I
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Solution
The correct options are A(adjM)2=I CdetM=1 DM2=I M−1=adj.(adj.M)=|M|3−2.M