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A 2x2 matrix transforms the unit square by mapping its standard basis vectors to the matrix's columns. The first column represents the image of the first basis vector, and the second column represents the image of the second basis vector.

Conditions: The matrix is 2x2.; The transformation is linear.; The unit square is defined by the standard basis vectors $e_1=(1,0)$ and $e_2=(0,1)$.

A 2x2 matrix transforms the unit square by mapping its standard basis vectors to the matrix's columns. The first column represents the image of the first basis vector, and the second column represents the image of the second basis vector.

Conditions: The matrix is 2x2.; The transformation is linear.; The unit square is defined by the standard basis vectors $e_1=(1,0)$ and $e_2=(0,1)$.