The point \(P(a, b)\) undergoes the following three transformations successively: (A) reflection about the line \(y=x\) …

The point \(P(a, b)\) undergoes the following three transformations successively:
(A) reflection about the line \(y=x\)
(B) translation through 2 units along the positive direction of \(x\)-axis.
(C) rotation through angle \(\frac{\pi}{4}\) about the origin in the anticlockwise direction.
If the co-ordinates of the final position of the point \(P\) are \(\left(-\frac{1}{\sqrt{2}}, \frac{7}{\sqrt{2}}\right)\) then the value of \(2 a+b\) is equal to:

[JEE Main 2021, 27 Jul (Shift 2)]