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If A = {:((1,-1),(1,2)):}and I={:((1,0),...

If `A = {:((1,-1),(1,2)):}`and `I={:((1,0),(0,1)):}` then `3A^(-1)` is equal to :

A

`3I-A`

B

`4I-A`

C

`6I-A`

D

`A - 6I`

Text Solution

Verified by Experts

The correct Answer is:
A
`A = ({:(1,-1),(1,2):})," |A|=3`
`A^(-1) = ("adj A")/(|A|)= (({:(2,1),(-1,2):}))/3`
`3 A^(-1)( {:(2,1),(-1,1):})=3I - A`
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(i) if A=[{:(1,0),(0,1):}],B=[{:(0,1),(1,0):}]and C=[{:(1,0),(0,1):}], then show that A^(2)=B^(2)=C^(2)=I_(2). (ii) if A=[{:(1,0),(1,1):}],B=[{:(2,0),(1,1):}]and C=[{:(-1,2),(3,1):}], then show that A(B+C)=AB+AC. (iii) if A=[{:(1,-1),(-1,1):}]and B=[{:(1,1),(1,1):}], then show that AB is a zero matrix.