Given Find B so that AB = I = BA as follows: First equate entries on the two...

You need to multiply the matrices A and B such
that:

= ((1,0,0),(0,1,0),(0,0,1))

4c+3f+2i),(5a+6d+3g, 5b+6e+3h, 5c+6f+3i),(3a+5d+2g, 3b+5+2h, 3c+5f+2i)) =
((1,0,0),(0,1,0),(0,0,1))

Equating corresponding terms
yields:

1

= 0

You need to
consider the equations that contain a,d,g such
that:

0

You need to subtract the third equation from the first
such that:

You
need to multiply the first equation by 3 and the second equation by -2 and then you
should add the new equations such that:

3

- 3d = 3

You need to multiply the equation a - 2d = 1 by
-2 such that:

-2

Adding this equation to 2a - 3d = 3
yields:

2

3

-7

You need to consider the equations that contain b,e,h
such that:

0

Subtracting the third equation from the first
yields:

2e

Substituting 2e for b in the first and second equations
yields:

3h = 1

You need to multiply by 3 the equation 11e + 2h = 0
and by -2 the equation 16e + 3h = 1 such that:

0

-32e - 6h = 0-2

-4

11

You need to consider the equations that contain c,f,i
such that:

1

-1

1

Substituting 2f - 1 for c in the first and second
equations yields:

5

10

2

3

-9

Hence, evaluating the matrix B under
given conditions yields