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Level 339

Matrix Multiplication, Inverses & Determinants

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Properties of Matrix Multiplication
For any matrices A, B, and C for which the matrix product is defined and any scalar k, the following properties are true.
(AB)C = A(BC)
Associative Property of Multiplication
k(AB) = (kA)B= A(kB)
Associative Property of Scalar Multiplication
Left Distributive Property
C(A+B) = CA + CB
Right Distributive Property
(A+B)C = AC + BC
identity matrix
diagonal matrix with ones in the leading diagonal and zeros in the other positions.
inverse matrix
The multiplicative inverse of a square matrix is called its inverse matrix.