Question

If $A^2=A$ and $(I+A{)}^4$ is equal to $I+kA$ then find $k$.

Answer 1

Answer: 15.00

$(I+A{)}^4=(I+A{)}^2\cdot (I+A{)}^2$
$=\left(I+2A+A^2\right)\cdot \left(I+2A+A^2\right)$
$=(I+3A)\cdot (I+3A)$
$=I+6A+9A^2$
$=I+6A+9A$
$=I+15A$