Question # Which of the following is/are incorrect?

# Which of the following is/are incorrect?

(A) Adjoint of a symmetric matrix is skew symmetric matrix.

(B) Adjoint of a diagonal matrix is a diagonal matrix.

( (mathrm{C}) mathrm{A}(mathrm{Adj} mathrm{A})=(mathrm{Ad} mathrm{i} mathrm{A}) mathrm{A}=1 mathrm{AII} )

(D) Adjoint of a unit matrix is a diagonal matrix

Solution

Properties

A (ad, A) = |A| Jn = (ad,A)A

( operatorname{lod}_{2} A_{1}=|A|^{n-1} )

( quad ) ads ( ^{circ} ) Cad ( g(A)=quad|A|^{n-2} ) o ( A )

( quadleft|operatorname{adg}left(a d_{3} Aright)right|=|A|^{(n-1)^{2}} )

( quad operatorname{adg}left(A^{top}right)=(dot{O} d g A)^{top} )

( quad ) odg ( (k A)=k^{n-1} )

( operatorname{adg}(0)=0 )

A is symmetoic Mathx ( Rightarrow ) adj A is also symmetric

A is diagomal Natain ( Rightarrow ) adj ( A ) is also diagonal

A is trianguar mabix ( Rightarrow ) adja is as Thangular