Question

Let A be an invertible 3x3 matrix, then det (A asj. A) is equal to?

Answer 1

Step-by-step explanation:

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

We know that, A⋅A−1=IA⋅A−1=I

⇒A⋅(adj(A)|A|)=I⇒A⋅(adj(A)|A|)=I

⇒A⋅adj(A)=|A|⋅I⇒A⋅adj(A)=|A|⋅I

⇒|A⋅adj(A)|=|A|n⇒|A⋅adj(A)|=|A|n

⇒|A|⋅|adj(A)|=|A|n⇒|A|⋅|adj(A)|=|A|n

⇒|adj(A)|=|A|n−1⇒|adj(A)|=|A|n−1

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

Answer 2

Answer:

refer to this image hope it will help you