If A is a square matrix such that \(A^2 = A\) and I is the identity matrix of the same order as A, then \((I + A)^2 - 3A\) is equal to
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(I\)
The identity matrix commutes with A (IA = AI = A), so the square can be expanded as for numbers:
\((I + A)^2 = I^2 + IA + AI + A^2 = I + 2A + A^2\)
Using \(A^2 = A\):
\((I + A)^2 = I + 3A\)
\((I + A)^2 - 3A = I\)