Evaluate (I + A)2 − 3A
Given:
\[ A^2 = A \]
Step 1: Expand
\[ (I + A)^2 = I^2 + IA + AI + A^2 \]
\[ = I + A + A + A^2 \]
\[ = I + 2A + A^2 \]
Step 2: Use A2 = A
\[ (I + A)^2 = I + 3A \]
Step 3: Subtract 3A
\[ (I + A)^2 – 3A = I + 3A – 3A = I \]
Final Answer:
\[ \boxed{I} \]