Single Choice

Let A be any $$3\times 3$$ invertible matrix. Then which one of the following is not always true?

A$$adj (adj (A))=|A|\cdot (adj(A))^{-1}$$
Correct Answer
B$$adj(adj(A))=|A|^2\cdot(adj(A))^{-1}$$
C$$adj(adj(A))=|A|\cdot A$$
D$$adj(A)=|A|\cdot A^{-1}$$

Solution

we know that A.adjA=|A|I2

adj(adj(A))=|A|n−2A=|A|3−2A=|A|.A so 3rd is correct

using adjA=|A|A−1.....4th is true

adj(adjA)=|adjA|(adjA)−1

=|A|2(adjA)−1

so 2nd is true

we can say 1 st is wrong option

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