Property of Matrix Multiplication

[Yankel]

Hello, I wanted to ask if this is a correct move, A and B are matrices, a is a scalar, thank you !

$$A^{2}\cdot B^{t}-aA=A(A\cdot B^{t}-aI)$$

 

[caffeinemachine]

Hello, I wanted to ask if this is a correct move, A and B are matrices, a is a scalar, thank you !

$$A^{2}\cdot B^{t}-aA=A(A\cdot B^{t}-aI)$$

Seems correct to me.

 

[Sudharaka]

Hello, I wanted to ask if this is a correct move, A and B are matrices, a is a scalar, thank you !

$$A^{2}\cdot B^{t}-aA=A(A\cdot B^{t}-aI)$$

Hi Yankel, :)

Yes, its correct because matrix multiplication is distributive over matrix addition.

Kind Regards,
Sudharaka.

 

[Yankel]

Thank you !

 

[blue_raver22]

Yes, this is a correct move in matrix multiplication. This property, known as the distributive property, allows us to factor out a common term from both matrices being multiplied. In this case, the common term is the matrix A. This property is useful in simplifying calculations and can also be extended to larger matrices and multiple terms being multiplied together. Overall, it is an important property to understand in order to effectively perform matrix multiplication.