If A is a square matrix such that A2 = A, then (I + A)3 − 7A is equal to

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KollegeApply · Accepted Answer

I Here, A^2 = A . . . \left( 1 ight) A^3 = A^2 A = A^2 \left[ 	ext{From eq }. \left( 1 ight) ight] = A 	herefore A^3 = A . . . \left( 2 ight) 	ext{We know that} \left( I + A ight)^3 = I^3 + 3 \left( I ight)^2 A + 3\left( I ight) A^2 + A^3 \Rightarrow \left( I + A ight)^3 = I + 3A + 3A + A \left[ 	ext{From eqs }. \left( 1 ight) and \left( 2 ight) ight] \Rightarrow \left( I + A ight)^3 = I + 7A \Rightarrow \left( I + A ight)^3 - 7A = I

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