Refer to the attachment.

Hope this helps!

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Verified answer

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To find (I + A)³ - 7A when A² = A, let's use the binomial expansion formula for (I + A)³:

(I + A)³ = I³ + 3I²A + 3IA² + A³

Since A² = A, we can simplify further:

(I + A)³ = I + 3IA + 3IA + A³

Now, subtract 7A:

(I + 3IA + 3IA + A³) - 7A = I + 6IA + A³ - 7A

Since A² = A, we can replace A³ with A in the expression:

I + 6IA + A - 7A

Now, combine like terms:

I + A - A = I

So, (I + A)³ - 7A is equal to I, which corresponds to option (d) "I."