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

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

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Given: `A=[(-1, 0, 0),( 0,-1, 0),( 0, 0,-1)]`
Then,
`A^2=[(-1, 0, 0),( 0,-1, 0),( 0, 0,-1)][(-1, 0, 0),( 0,-1, 0),( 0, 0,-1)]`

`A^2=[(1+0+0,0+0+0,0+0+0),(0+0+0,0+1+0,0+0+0),(0+0+0,0+0+0,0+0+1)]`

`A^2=[(1,0,0),(0,1,0),(0,0,1)]`
Then
...
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RD SHARMA-ALGEBRA OF MATRICES-Solved Examples And Exercises
  1. If A=[1 1 1 1] satisfies A^4=lambdaA , then write the value of lambda

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

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

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

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

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

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  7. Find a matrix A ,ifA+[2 3-1 4]=[3-6-3 8]

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  8. If A=[a(i j)] is a square matrix such that a(i j)=i^2-j^2 , then wr...

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  9. For any square matrix write whether AA^T is symmetric or skew-symm...

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  10. If A=[a(i j)] is a skew-symmetric matrix, then write the value of s...

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  11. If A=[a(i j)] is a skew-symmetric matrix, then write the value of s...

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  12. If A and B are symmetric matrices, then write the condition for whi...

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  13. If B is a skew-symmetric matrix, write whether the matrix A B\ A^T ...

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  14. If B is a symmetric matrix, write whether the matrix A B\ A^T is sy...

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  15. If A is a skew-symmetric and n in N such that (A^n)^T=lambda\ A^n ...

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  16. If A is a symmetric matrix and n in N , write whether A^n is symme...

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  17. If A is a skew-symmetric matrix and n is an even natural number,...

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  18. If A and B are symmetric matrices of the same order, write whether ...

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  19. Write a square matrix which is both symmetric as well as skew-symme...

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  20. Find the values of x and y , if 2[(1, 3),( 0,x)]+[(y,0),( 1, 2)]=[(5...

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