Finding a matrix to represent a 2x2 transpose mapping

[PsychonautQQ]

Homework Statement

Let L be a mapping such that L(A) = A^t, the transpose mapping. Find a matrix representing L with respect to the standard basis [1,1,1,1]

Homework Equations

The Attempt at a Solution

So should I end up getting a 4x4 matrix here? I got 1,0,0,0 for the first column, 0,0,1,0 for the second column, 0,1,0,0 for the third column and 0,0,0,1 for the fourth column. is this correct?

 

[Mark44]

Homework Statement

Let L be a mapping such that L(A) = A^t, the transpose mapping. Find a matrix representing L with respect to the standard basis [1,1,1,1]

How is [1, 1, 1, 1] a basis?
I think you mean {<1, 0, 0, 0>, <0, 1, 0, 0>, <0, 0, 1, 0>, <0, 0, 0, 1>}.

Homework Equations

The Attempt at a Solution

So should I end up getting a 4x4 matrix here? I got 1,0,0,0 for the first column, 0,0,1,0 for the second column, 0,1,0,0 for the third column and 0,0,0,1 for the fourth column. is this correct?

This works, if it's legitimate to work with vectors in $\mathbb{R}^4$ instead of 2 x 2 matrices. Of course $\mathbb{M}_{2 x 2}$ is isomorphic to $\mathbb{R}^4$. Based on what I think the problem statement is supposed to mean, your solution looks fine.