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Consider the following in respect of the...

Consider the following in respect of the matrix `A=({:(-1,1),(1,-1):})`:
1. `A^(2)=-A`
2. `A^(3)=4A`
Which of the above is/are correct ?

A

1 only

B

2 only

C

Both 1 and 2

D

Neither 1 nor 2

Text Solution

Verified by Experts

The correct Answer is:
B
`A=[(-1,1),(1,-1)]`
`A.A=[(-1,1),(1,-1)][(-1,1),(1,-1)]`
`=[(2,-2),(-2,2)]=-2[(-1,1),(1,-1)]`
`A^(2)=-2A`
`A^(2).A=-2[(-1,1),(1,-1)][(-1,1),(1,-1)]`
`=-2[(2,-2),(-2,2)]=4[(-1,1),(1,-1)]`
`A^(3)=4A`
Hence `A^(2)ne -A,A^(3)=4A`
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