If angular momentum is conserved in a system whose moment of inertia is decreased, Will its rotational kinetic energy be also conserved? Explain.

L= Iw
where ,
L is angular momentum.
I is moment of Inertia
w is angular momentum.
I₁w₁ = I₂w2
or I1w1/I2w2 = 1   ............(1)
Now lets check for Rotaional Kinetic energy 
1/2 I1​w1​2 / 1/2 I2 w22  

=$\frac{I_1{w_1}^2}{I_2{w_2}^2} = \raisebox{1ex}{$w_1$}\!\left/ \!\raisebox{-1ex}{$w_2$}\right. \ne 1$
so ​rotational kinetic energy not conserved