What is the formula for Det[ adj( adj(A) ) ] and how do you derive it ? Share with your friends Share 4 Vipin Verma answered this First find adj(adjA)we know that A-1 =adjAA⇒adjA=AA-1 .......1Multiply both sides by adjA-1 , we getadjA-1 adjA = adjA-1 AA-1⇒I =adjA-1 A A-1 as, I is the identity matrixMultiplying both sides by A , we get ⇒I A =adjA-1 A A-1 A ⇒I A = adjA-1 A I⇒A = adjA-1 A divide both sides by A, we getAA = adjA-1 ......2To find the inverse of adjA , apply general formula of finding inverse.adjA-1=adjadjAadjA⇒adjA (adj(A))-1 =adjadjAAs, adjA =An-1 ........3So using 2 and 3, we haveadj(adj(A) =An-1 .AA =An-2 ASo, adjadjA =An-2 AAs the quantity in the bracket has An-2 , it is a constant term , so , An-2 = An-2So, adjadjA = An-2 A = An-1 -13 View Full Answer
