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OK I already have the answer for this problem but I don't know how my teacher came up with the answer:

Linear transformation T in R^3 consists of the rotation around x3 axis at the positive (counter-clockwise) direction at the angle 90 degrees. Such rotation transforms x1-axis into x2-axis. Find the matrix of this transformation.

Diagram for this problem is attached.

Also, the answer is:

[0 -1 0]

[1 0 0]

[0 0 1]

Linear transformation T in R^3 consists of the rotation around x3 axis at the positive (counter-clockwise) direction at the angle 90 degrees. Such rotation transforms x1-axis into x2-axis. Find the matrix of this transformation.

Diagram for this problem is attached.

Also, the answer is:

[0 -1 0]

[1 0 0]

[0 0 1]