No, it is a linear transformation.
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Linear system has a proportional slope, which gives the system a straight line. And, a non-linear system has a non-proportional slope, which is represented by a non-straight line (usually a curved one). Feel free to edit if you think this is not to the point.
When its matrix is non-singular.
non linear
When its determinant is non-zero. or When it is a linear transform of the identity matrix. or When its rows are independent. or When its columns are independent. These are equivalent statements.
Usually non-linear.Usually non-linear.Usually non-linear.Usually non-linear.