Matrix筆記

Property of multiplication

The commutative property of multiplication $\small{\red{\text{does not hold!}}}$	$AB\neq BA$A, B, does not equal, B, A
Associative property of multiplication	$(AB)C=A(BC)$left parenthesis, A, B, right parenthesis, C, equals, A, left parenthesis, B, C, right parenthesis
Distributive properties	$A(B+C)=AB+AC$A, left parenthesis, B, plus, C, right parenthesis, equals, A, B, plus, A, C
	$(B+C)A=BA+CA$left parenthesis, B, plus, C, right parenthesis, A, equals, B, A, plus, C, A
Multiplicative identity property	$IA=A$I, A, equals, A and $AI=A$A, I, equals, A
Multiplicative property of zero	$O A=O$O, A, equals, O and $AO=O$A, O, equals, O
Dimension property	The product of an $m\times n$m, times, n matrix and an$n\times k$n, times, k matrix is an $m\times k$m, times, k matrix.