Properties of Matrix Operations

Associative Property of Matrix Addition

• A + B = B + A
• (A + B) + C = A + (B + C)
• AB = BA
• A + 0 = A

Tags

CCSS.HSN.VM.C.8

(AB)C=A(BC)

• Distributive Property of Matrix Multiplication
• Commutative Property of Matrix Multiplication
• Associative Property of Matrix Multiplication
• Associative Property of Scaler Multiplication

Tags

CCSS.HSN.VM.C.9

(cd)A = c(dA)

• distributive property of scalar multiplication

• Associative property of scalar multiplication

• commutative property of scalar multiplication

• Scalar identity property

Tags

CCSS.HSN.VM.C.9

c(AB)=(cA)B

• Distributive property of matrix multiplication

• distributive property of scalars

• Commutative property of scalar multiplication

• Associative property of scalar multiplication

Tags

CCSS.HSN.VM.C.9

Scalar Identity Property

• A+(-A)=0

• 1A=A

• A+0=A

• AB+BA

Tags

CCSS.HSN.VM.C.10

(c+d)A = cA + dA

• Scalar Identity

• Commutative property of scalars

• Associative property of scalars

• Distributive property of scalars

A + 0 = A

• Scalar Identity

• Additive Inverse

• Additive Identity

• Scalar Inverse

Tags

CCSS.7.NS.A.1B

Additive Inverse Property

• A + 0 = A
• A + (-A) = 0
• 1A = A
• A + B = B + A 

Tags

CCSS.7.NS.A.1B

(A + B)C = AC + BC

• Commutative Property of Matrix Multiplication
• Distributive Property of Matrix Multiplication
• Associative Property of Matrix Multiplication
• Commutative Property of Matrix Addition

Tags

CCSS.HSN.VM.C.9

Which of the following is NOT a property of matrix operations?

• A + B = B + A 
• AB = BA 
• (AB)C = A(BC)
• (A + B) + C = A + (B + C)

Tags

CCSS.HSN.VM.C.9