Question

if A is a square matrix of order 3 such that |A| = 5 , find |A.adjA| .​

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

Step-by-step explanation: