If A is square matrix such that A2 = A, then (I + A)3 - 7A is equal to:
Answer & explanation
Correct answer: option 3
Given
$A^2=A$
Find $(I+A)^3$
$(I+A)^3=I^3+3I^2A+3IA^2+A^3$
$=I+3A+3A^2+A^3$
Since $A^2=A$
$A^3=A\cdot A^2=A\cdot A=A$
So
$(I+A)^3=I+3A+3A+A$
$=I+7A$
Now
$(I+A)^3-7A=(I+7A)-7A$
$=I$
The value is $I$ (identity matrix).