Question

If A is a square matrix of order 3 such that A(adj A) = 10 I where I is the identity matrix of order 3, then |adj A|
is equal to.​

Answer 1

Answer:

|adj A|=(10)^(2/3)

Step-by-step explanation:

A(adj A) =10 I

So,

|A(adj A) |=10

|A|×|(adj A) |=10

Now, |(adj A)|=|A|^(n-1)

Where n is the order of the matrix,

Here n=3 so,

|adj A|=|A|^2

i.e

|A|×|A|^2=|A|^3=10

|A|=(10)^(1/3)

So

|adj A|=(10)^(2/3)