If A is a square matrix such that $A^2=A$ and $I$ is the identify matrix of the same order as $A$ then $(I + 2A)^3-6A$ is equal to

$I + 20A$

The correct answer is Option (3) → $I + 20A$ **

$A^2=A$

$(I+2A)^3 = I + 6A + 12A^2 + 8A^3$

Since $A^2=A$ and $A^3=A$:

$(I+2A)^3 = I + 6A + 12A + 8A = I + 26A$

Therefore,

$(I+2A)^3 - 6A = I + 26A - 6A = I + 20A$