Show that B is the inverse of A.

Question

A = -1/2 -5/4 B = 8 5

1 2 -4 -2

To show that B is the inverse of A, we need to show that AB = I = BA.

AB = -4 + ___ -5/2 + ___ = ____ ____

8 + ___ 5 + ___ ____ ____

BA = -4 + ___ -10 + ___ = ____ ____

2 + ___ 5 + ___ ____ ____

Answer 1

A1 A2 B1 B2

[ -1/2 -5/4 ] [ 8 5 ]

[ 1 2 ] [ -4 -2 ]

A*B

row 1, column 1

(-1/2)(8) + (-5/4)(-4) = -4 + 5 = 1 <--- yes

row 2,column 1

(1)(8) + 2 (-4) = 8 + -8 = 0 <--- yes

row 1 , column 2

(-1/2)(5) + (-5/4)(-2) = -5/2 + 5/2 = 0 <--- yes

row 2, column 2

(1)(5) + 2(-2) = 5-4 = 1 <--- yes

B*A

(8)(-1/2) + (-4)(*-5/4) = -4 +5 = 1

(8)(1) + 2(-4) = 0

(5)(-1/2) + (-5/4)(-2) = -5/2+5/2 = 0

(5)(1) + (2)(-2) = 5 - 4 = 1