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If matrix A=[[1,-1],[-1 ,1]] and A^2=k A...

If matrix `A=[[1,-1],[-1 ,1]]` and `A^2=k A ,` then write the value of `k`

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Given: `A=[[1,-1],[-1 ,1]]` and `A^2=k A`
Then,
`A^2=[(1,-1),(-1 ,1)][(1,-1),(-1 ,1)]`
`A^2=[(1xx1+(-1)xx(-1)),1xx(-1)+(-1)xx1,((-1)xx1+1xx(-1),(-1)xx(-1)+1xx1)]`
`A^2=[(2,-2),(-2,2)]`
As `A^2=k A`
Then
`[(2,-2),(-2,2)]=K[(1,-1),(-1,1)]`
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RD SHARMA-ALGEBRA OF MATRICES-Solved Examples And Exercises
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  2. If [(1, 0),(y,5)]+2[(x,0),( 1,-2)]=I , where I is 2xx2 unit matrix. Fi...

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  3. If matrix A=[[1,-1],[-1 ,1]] and A^2=k A , then write the value of k

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  4. If A=[1 1 1 1] satisfies A^4=lambdaA , then write the value of lambda

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  5. If A=[-1 0 0 0-1 0 0 0-1] , find A^2 .

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  6. If A=[-1 0 0 0-1 0 0 0-1] , find A^3 .

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  7. If A=[-3 0 0-3] , find A^4 .

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  8. If [[x,2]][[3],[ 4]]=2, find x

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  9. If A=[a(i j)] is a 2xx2 matrix such that a(i j)=i+2j , write A .

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