Question

If a is matrix of order 3 and determinant of a is 5 find determinent of adj a

Answer 1

Answer:

Given matrix A of order n, A−1=adj(A)|A|;

We know that, A⋅A−1=I

⇒A⋅(adj(A)|A|)=I

⇒A⋅adj(A)=|A|⋅I

⇒|A⋅adj(A)|=|A|n

⇒|A|⋅|adj(A)|=|A|n

⇒|adj(A)|=|A|n−1

Therefore, here |adj(A)|=52=25

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