Question

Verify that A and B are inverses of each other by finding AB A=[3 8], B=[-1 4] [1 2]. [1/2 -3/2] AB=

Answer 1

Answer:

We conclude that A and B are inverses of each other since the product AB gives an identity matrix

Step-by-step explanation:

If A and B are inverses of each other, then

`AB=\begin{bmatrix}{1} & {0} \\ {0} & {1}\end{bmatrix}`

`\begin{gathered} AB=\begin{bmatrix}{3} & {8} \\ {1} & {2}\end{bmatrix}\begin{bmatrix}-{1} & {4} \\ {(1)/(2)} & {-(3)/(2)}\end{bmatrix} \\ \\ =\begin{bmatrix}{-3+(8)/(2)} & 12-(24)/(2){} \\ {-1+(2)/(2)} & 4-(6)/(2){}\end{bmatrix} \\ \\ =\begin{bmatrix}{1} & {0} \\ {0} & {1}\end{bmatrix} \end{gathered}`

Therefore, we conclude that A and B are inverses of each other.