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Question

If A is an idempotent matrix satisfying, (I0.4A)1=IαA, where I is the unit matrix of the same order as that of A, then the value of |9α| is equal to ..............

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Solution

A is an idempotent matrix i.e A2=A(I0.4A)1=IαAI=(IαA)(I0.4A)=I20.4AIαAI+0.4αA2=I+A(0.40.6α)α=46Hence|9α|=6

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