Q. 35

# If A = <img

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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