Question

If A is a square matrix of order 3, such that A(adjA) =10I , then (adjA) is equal to​

Answer 1

Step-by-step explanation:

Given If A is a square matrix of order 3, such that A(adjA) =10 I , then (adjA) is equal to

• Consider the equation A (adj A) = lAl I
• Given A (adj A) = 10 I
• Comparing this with the general equation we get
• So l A l = 10
• We know that ladj Al = l Al^n-1 where n is the order of matrix.
•                                  = l A l ^3 -1 (since order of matrix is 3)
•                                  = l Al^2
•                                   = 10^2
•                                  = 100

Reference link will be

https://brainly.in/question/9949388

Answer 2

A is a square matrix of order 3, such that A(adjA) =10I , then (adjA) is equal to​

Given,

A(adjA) =10I

⇒ |A| = 10

We have formula for calculating the adjoint of a matrix, given by,

|adj (A)| = |A|^{n-1}

where, n = order of the square matrix

As given n = 3, so we get,

|adj (A)| = |A|^{3-1}

|adj (A)| = |A|^{2}

as |A| = 10

|A|^{2} = 10^2

|A|^{2} = 100

Therefore (adjA) is equal to​ 100