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Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.
Add, subtract, and multiply matrices of appropriate dimensions.
Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.
Work with 2 × 2 matrices as a transformations of the plane, and interpret the absolute value of the determinant in terms of area.