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Find the matrix A satisfying the matrix ...

Find the matrix A satisfying the matrix equation
`[{:(2,1),(3,2):}]A[{:(-3,2) ,(5,-3):}]=[{:(1,0),(0,1):}]`

A

`[(1,1),(1,0)]`

B

`[(1,1),(0,1)]`

C

`[(1,0),(1,1)]`

D

`-[(1,1),(1,0)]`

Text Solution

Verified by Experts

The correct Answer is:
A
`[(2,1),(3,2)]A[(-3,2),(5,-3)]=[(1,0),(0,1)]`
`A=[(2,1),(3,2)]^(-1) [(1,0),(0,1)][(-3,2),(5,-3)]^(-1)`
`=[(2,-1),(-3,2)][(1,0),(0,1)] [(-3,-2),(-5,-3)]`
`=[(2,-1),(-3,2)][(3,2),(5,3)]=[(1,1),(1,0)]`
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