"why here it is not returning true"

(a && a["c"]) returns a if a is falsy and a["c"] if a is truthy. An object is always truthy, therefore (a && a["c"]) returns "b".

"How to return a boolean from a value here"

!! is a common operation to convert a truthy value to true and a falsy value to false.

"is it correct way to return true or any other better way available?"

It is correct and I would use !!(a && a["c"]) to convert (a && a["c"]) to boolean.

You can make it shorter with !!a?.c (optional chaining):

<button title="Submit" *ngIf="!!a?.c">Submit</button>

or even

<button title="Submit" *ngIf="a?.c">Submit</button>

if your TypeScript configuration allows it.

I recommend to check the list of truthy and falsy values. Sometimes the results can be very surprising.