If $A$ is a square matrix such that $A^2=A$ and $I$ is the identity matrix of the same order as $A$, then $(I+2A)^2 - 5A$ is equal to
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $I+3A$ **
Given: $A^{2}=A$
Compute $(I+2A)^{2}$:
$(I+2A)^{2}=I^{2}+4A+4A^{2}$
$=I+4A+4A$ (since $A^{2}=A$)
$=I+8A$
Now subtract $5A$:
$(I+2A)^{2}-5A = (I+8A)-5A$
$=I+3A$
$I+3A$