# Property of Matrix Multiplication

#### Yankel

##### Active member
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

##### Well-known member
MHB Math Scholar
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

##### Well-known member
MHB Math Helper
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.

Thank you !