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?

1 Answer
sente
Apr 4, 2016

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

Explanation:

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))#

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