How do I create a list of matrices based on lists I have?

Question

Okay, so let's say I have these lists and a number

a = {1, 2, 3};
b = {4, 5, 6};

And now I want to create 3 matrices that each look like this

M = {{n^2 - b^2, a*b}, {b*a, n^2 - a^2}}

My desired output is that M is a list of 3 matrices, where

M = {M[[1]], M[[2]], M[[3]]}

and

M[[i]] = {{n^2 - b[[i]]^2, a[[i]]*b[[i]]}, {b[[i]]*a[[i]], n^2 - a[[i]]^2}}

I know I could use Table to do this, but I guess there is a more elegant method. Thanks!

Answer 1

One can do one of the three following, among others:

{{n^2 - #2^2, #1 #2}, {#2 #1, n^2 - #1^2}} & @@@ Transpose[{a, b}]

Table[{{n^2 - b[[i]]^2, a[[i]] b[[i]]}, {a[[i]] b[[i]], n^2 - a[[i]]^2}}, {i, 1, Length@a}]

MapThread[{{n^2 - #2^2, #1 #2}, {#2 #1, n^2 - #1^2}} &, {a, b}]

Answer 2

a = {1, 2, 3};
b = {4, 5, 6};
Transpose@MapThread[List, {{n^2 - b^2, a*b}, {b*a, n^2 - a^2}}, 2]