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Q.

If A is a non-zero matrix such that A2=A , satisfving (I−λA)−1=I−3A, where I is unit matrix of same order as that of A, then the value of λ , where |I−λA|≠0 is

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answer is 1.5.

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Detailed Solution

(I−λA)−1=(I−5A)∴I=(I−3A)(I−λA)⇒I=I−λA−3A+3λA2⇒O=−λA−3A+3λA⇒(2λ−3)A=O⇒2λ−3=0⇒λ=1.5

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