Casual system : when the output is given for present and past input for all values of n is called as causal system . In this case take some example value of n.
let say
n=1
y(1)=1.x(1)
that is output depends on present input
if n=0
y(0)= 0
if n=3
y(3)=3.x(3)
thus for all values of n the output is dependent on present input.
thus the ans is causal system

Definition of Causality

The causality of a system refers to whether the output of the system depends only on the present and past values of the input, or if it also depends on future values of the input. In other words, a causal system is one in which the output at any given time depends only on the input values up to that time.

Explanation

To determine the causality of the given system y[n] = n*x[n], let's analyze the equation and understand its behavior.

System Equation
y[n] = n*x[n]

Analysis:
- In the given equation, y[n] is the output and x[n] is the input.
- The system multiplies each sample of the input x[n] with the corresponding sample number n.
- This means that the output at any given time depends on the present value of the input and the current sample number.
- Since the output depends only on the present and past values of the input and not on any future values, we can conclude that the system is causal.

Reasoning:
- Causality requires that the output at any given time depends only on the present and past values of the input.
- In the given system, y[n] is directly proportional to the sample number n and the input sample x[n].
- As there is no dependence on any future values of the input, the system is causal.

Conclusion:
The given system y[n] = n*x[n] is causal because the output at any given time depends only on the present and past values of the input. Therefore, the correct answer is option 'd' - causal.