## frank0520 one year ago A=-3 1 1 | 1 -3 1|  1 1 -3 Calculate A(A+5I) and use the result to find the inverse of A.

1. frank0520

I got: -4 0 0 | 0 -4 0|  0 0 -4 for the computation. And I got: -1/4 0 0 | 0 -1/4 0|  0 0 -1/4 for the inverse. Is this the correct inverse?

2. jim_thompson5910

I'm getting $\Large A(A+5I) = \begin{bmatrix}-4 & 0 & 0\\0 & -4 & 0\\0 & 0 & -4\\ \end{bmatrix}$ as well

3. jim_thompson5910

I don't agree with your inverse though. I'm getting a different matrix for $$\Large A^{-1}$$

4. jim_thompson5910

To check, the product of $$\Large A$$ and $$\Large A^{-1}$$ (in either order) should be equal to $\Large I_3 = \begin{bmatrix}1 & 0 & 0\\0 & 1 & 0\\0 & 0 & 1\end{bmatrix}$

5. frank0520

@jim_thompson5910 I did the inverse of the computation. I also did the inverse of just A and got: $\left[\begin{matrix}-1/2 & -1/4 & -1/4 \\ -1/4 & -1/2 & -1/4 \\ -1/4 & -1/4 & -1/2\end{matrix}\right]$ I did the product of $A \ and\ A^-1$ and got the $I_3$ matrix.

6. jim_thompson5910

You have the correct inverse

7. jim_thompson5910

I'm not sure how Calculate A(A+5I) and use the result to find the inverse of A. fits into finding the inverse of A though

8. frank0520

@jim_thompson5910 Thanks for the help! I'm not sure either, maybe its just worded wrong.

9. jim_thompson5910

you're welcome