Question

if the value of third order determinants is 16 then the value of the determinants formed by replacing each of the its elements by its cofactor is​

Answer 1

Given :

The value of determinant of third order matrix (lAI)= 16

To Find:

The value of determinant by replacing elements with its cofactors

Solution :

• The matrix formed by replacing its elements by its cofactors is called as Adjoint matrix

• Let A be the matrix of order n,then we have the relation

             IadjAI = IAIⁿ⁻¹

             IadjAI = IAI³⁻¹

             IadjAI = (16)³⁻¹

             IadjAI = (16)²

             IadjAI = 196

  The value of the determinant is 196