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What is the inverse of A=[{:(0,0,1),(0,1...

What is the inverse of `A=[{:(0,0,1),(0,1,0),(1,0,0):}]`?

A

`[{:(1,0,0),(0,1,0),(0,0,1):}]`

B

`[{:(0,0,1),(0,1,0),(1,0,0):}]`

C

`[{:(-1,0,1),(0,-1,0),(0,0,-1):}]`

D

`[{:(0,0,-1),(0,-1,0),(-1,0,0):}]`

Text Solution

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The correct Answer is:
B
`A=[{:(0,0,1),(0,1,0),(1,0,0):}]`
`therefore |A|=[0(0)-0(0)+1(-1)]=-1`
and adj `A=[{:(0,0,-1),(0,-1,0),(-1,0,0):}]`
Hence, `A^(-1)=(1)/(|A|)`adj A
`=-(1)/(1)[{:(0,0,-1),(0,-1,0),(-1,0,0):}]=[{:(0,0,1),(0,1,0),(1,0,0):}]`
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