A is a 3x3 matrix and $A^-1 = ([3, 0, -1],[0, 8, 7],[-2, 3, 4])$ . If B is another matrix and $BA = ([4, -3, 7],[-1, 0, 2])$ , how do you find the matrix B?

Question

2228 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-04-04T10:05:20

$B=((-2,-3,3),(-7,6,9))$

Note that $A A^-1 = I$ where $I$ is the $3"x"3$ identity matrix. As matrix multiplication is associative, we have

$(BA) A^(-1) = B(A A^(-1)) = BI = B$

Thus, to find $B$ , we can simply multiply $BA$ by $A^(-1)$ . Doing so, we have:

$B=BA A^(-1)$

$= ((4, -3, 7),(-1,0,2))((3, 0, -1),(0, 8, 7), (-2, 3, 4))$

$=((-2,-3,3),(-7,6,9))$

A is a 3x3 matrix and A^-1 = ([3, 0, -1],[0, 8, 7],[-2, 3, 4])A^-1 = ([3, 0, -1],[0, 8, 7],[-2, 3, 4]). If B is another matrix and BA = ([4, -3, 7],[-1, 0, 2])BA = ([4, -3, 7],[-1, 0, 2]), how do you find the matrix B?