Finer grained standards that are part of this one
Work with 2 × 2 matrices as transformations of the plane and interpret the absolute value of the determinant in terms of area.
Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.
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.
Add, subtract, and multiply matrices of appropriate dimensions.
Understand that, unlike the multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.
Use matrices to represent and manipulate data, e.g., as when all of the payoffs or incidence relationships in a network.
Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimension to produce another vector. Work with matrices as transformations of vectors.