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If A is a square matrix such that A^2 = A, then write the value of (I + A)^2 - 3A.

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If A is a square matrix such that A2 = A, then write the value of (I + A)2 - 3A.

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1 Answer

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Best answer

Given A2 = A

(I+A)2-3A=?

= I2 + A2 + 2IA - 3A { (a+b)2=a2+b2+2ab }

IA=A (by property)

Since A2=A and IA=A and I2=I

= I+2A+A−3A

= I

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