If A is a square matrix and I is an identity matrix of same order such that \(A^2=A\), then \((2I+A)^2 - 5A\) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 4I
Since I commutes with A (\(IA = AI = A\)), the square expands as for numbers:
\((2I + A)^2 = 4I^2 + 2(2I)A + A^2\)
\(= 4I + 4A + A^2\)
Using \(A^2 = A\):
\(= 4I + 5A\)
\((2I + A)^2 - 5A = 4I\)