# Thread: Matrix problem: Finding all matrices A such that AM = - MA

1. ## Matrix problem: Finding all matrices A such that AM = - MA

Hiya, I'm stuck on this question and would be really grateful if someone could help me out here...

Let $M = \begin{bmatrix}7 & -3\\15 &-7 \end{bmatrix}$. Find all 2x2 matrices $A = \begin{bmatrix}a & b\\b &d \end{bmatrix}$ such that AM = - MA. (Note that the solutions wanted should have equal (1,2)- and (2,1)- entries b.)

I tried evaluating the equation AM= -MA via matrix multiplication and making equations out of the corresponding entries but ended up with something that just seemed completely wrong AND didn't have equal (1,2)- and (2,1)- entries.

rorosingsong.

2. Originally Posted by rorosingsong
Hiya, I'm stuck on this question and would be really grateful if someone could help me out here...

Let $M = \begin{bmatrix}7 & -3\\15 &-7 \end{bmatrix}$. Find all 2x2 matrices $A = \begin{bmatrix}a & b\\b &d \end{bmatrix}$ such that AM = - MA. (Note that the solutions wanted should have equal (1,2)- and (2,1)- entries b.)

I tried evaluating the equation AM= -MA via matrix multiplication and making equations out of the corresponding entries but ended up with something that just seemed completely wrong AND didn't have equal (1,2)- and (2,1)- entries.

rorosingsong.
Your method is correct just be really careful.

Here is a .pdf No work is shown but it does have the correct answer. It is a maple screen shot.

Matrix.pdf

3. oh wow, thanks so much!
I'll be more careful with the working this time. Cheers, I really appreciate your prompt reply, very helpful. =)