Question

If A is the matrix of order 3×3 with det|A| =5 then find the value of adj[adj(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

I hope it will help you....