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  • Definition of matrix multiplication in terms of column vectors
  • Definition of matrix multiplication
  • Theorem describing matrix multiplication
  • Any matrix times the 0 matrix equals the 0 matrix.
  • Example of multiplying 2x2 matrices
  • Example of multiplying 3x3 matrices
  • Example of multiplying nonsquare matrices
  • Example of multiplying matrices
  • Matrix multiplication is associative.
  • Matrix multiplication is distributive over matrix addition.
  • The identity matrix is the identity for matrix multiplication.
  • Matrix multiplication is not commutative in general.
  • Matrix cancellation requires an invertibility or rank hypothesis
  • Matrix multiplication can be viewed as the dot product of a row vector of column vectors with a column vector of row vectors
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  1. Any matrix times the 0 matrix equals the 0 matrix.

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  • Definition of 0 matrixClose match
  • Example of multiplying nonsquare matricesClose match
  • Matrix addition is commutative and associative.Close match
  • A matrix with a 0 row/column has determinant 0Close match
  • Matrix multiplication is associative.Close match
  • Matrix-scalar multiplication is commutativeClose match
  • Matrix multiplication is distributive over matrix addition.Close match
  • Matrix multiplication is not commutative in general.Close match
  • The 0 scalar multiplied by any vector equals the 0 vector.Close match
  • Matrix multiplication can be viewed as the dot product of a row vector of column vectors with a column vector of row vectorsClose match
  • Example of multiplying 2x2 matricesClose match
  • The 0 vector is unique.Close match
  • Matrix-vector product is associativeClose match
  • If two matrices have equal products with all vectorsClose match
  • Matrix-vector productsClose match
  • Definition of matrix multiplication in terms of column vectorsClose match
  • Example of multiplying matricesClose match
  • Equivalence theorem for nonsingular matrices: the null space of the matrix A is {0}.Close match
  • The identity matrix is the identity for matrix multiplication.Close match
  • Theorem describing matrix multiplicationClose match

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