Question

If A is a 3x3 matsin such that
|Al=5, what is the value of |2A|?​

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