Convolution Properties and Fourier Transform

[Pewgs]

Homework Statement

Determine whether the assertions are true or false, explain.
(a) If (f * g)(t) = f(t), then g(t) must be an impulse, d(t).
(b) If the convolution of two functions f1(t) and f2(t) is identically zero,
(f1 * f2)(t) = 0
then either f1(t) or f2(t) is identically zero, or both are identically zero.

Homework Equations

Fourier Transform implies that Xf1(jw)*Xf2(jw)=transform on the convolution.

The Attempt at a Solution

a) If Xf1(jw)*Xf2(jw)=Xf1(jw) then Xf2(jw) must be equal to 1, which is the same as d(t).

Not sure about b...

 

[I like Serena]

Welcome to PF, Pewgs!

Your (a) looks good!

For (b) you should perhaps consider 2 transforms that multiply to zero, but are not zero themselves.
For instance a Heaviside function and its mirror.