Answer :

Given:

To find: value of λ


Given equation: A2 = λA – 2I


Firstly, we find the A2





Putting the values in given equation


A2 = λA – 2I






On Comparing, we get


3λ – 2 = 1 …(i)


-2λ = -2 …(ii)


4λ = 4 …(iii)


-2λ – 2 = -4 …(iv)


Solving eq. (iii), we get


4λ = 4


λ = 1


Hence, the value of λ = 1


So, the given equation become A2 = A – 2I


Now, we have to find A-1


Finding A-1 using given equation


A2 = A – 2I


Post multiplying by A-1 both sides, we get


(A2)A-1 = (A – 2I) A-1


A2.A-1 = AA-1 – 2IA-1


A.(AA-1) = I – 2A-1 [AA-1 = I]


A(I) = I – 2A-1


A + 2A-1 = I


2A-1 = – A + I







Ans. λ= 1, A-1 = .


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