4333.sagews

# 17

A = matrix(QQ,[[1,-3],[-3,5]]);A

[ 1 -3] [-3 5]

# Let B = [[b1,b2],[b3,b4]]
var('b1,b2,b3,b4')
B = matrix(SR,[[b1,b2],[b3,b4]]); B

[b1 b2] [b3 b4]

# We are given the result of AB. If we multiply A and B above, we get a system of equations, which we'll represent in augmented matrix form:
    
AB = matrix(QQ,[[1,0,-3,0,-3],[-3,0,1,0,1],[0,1,0,-3,-11],[0,-3,0,5,17]]);AB

[ 1 0 -3 0 -3] [ -3 0 1 0 1] [ 0 1 0 -3 -11] [ 0 -3 0 5 17]

# row reducing we find the values of b1,b2,b3,b4 in B.
AB.rref()

[1 0 0 0 0] [0 1 0 0 1] [0 0 1 0 1] [0 0 0 1 4]