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If matrix A=[a(ij)](2X2), where a(ij)=...

If matrix `A=[a_(ij)]_(2X2)`, where ` a_(ij)={[1,i!=j],[0,i=j]}, then A^2` is equal to

A

I

B

A

C

0

D

none of these

Text Solution

Verified by Experts

We have, `A=[a_(ij)]_(2xx2)`, where `a_(ij)=1`, if `inej=0` and if i=j
`A=[{:(0,1),(1,0):}]`
and `A^(2)=[{:(0,1),(1,0):}][{:(0,1),(1,0):}]=[{:(1,0),(0,1):}]=I`
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NCERT EXEMPLAR-MATRICES-Matrices
  1. If A and B are two matrices of the order 3 xx m and 3 xx n, respective...

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  2. If A=[{:(0,1),(1,0):}] then A^(2) is equal to

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  3. If matrix A=[a(ij)](2X2), where a(ij)={[1,i!=j],[0,i=j]}, then A^2 i...

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  4. The matrix [{:(1,0,0),(0,2,0),(0,0,4):}] is a

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  5. The matrix [{:(0,-5,8),(5,0,12),(-8,-12,0):}] is a

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  6. If A is matrix of order mxxn and B is a matrix such that AB' and B'A ...

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  7. if A and B are matrices of same order, then (AB'-BA') is a 1) null mat...

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  8. If A is a square matrix such that A^(2)= I, then (A-I)^(3)+(A+I)^(3)...

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  9. For any two matrices A and B , we have

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  10. On usign elementry column operation C(2)rArrC(2)-2C(1) in the followin...

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  11. On using row operation R(1)rArrR(1)-3R(2) in the following matrix equa...

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  12. ......... Matrix is both symmetric and skew-symmetric matrix.

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  13. Sum of two skew-symmetric matrices is always ......... Matrix.

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  14. The negative of a matrix is obtained b y multiplying it by ...........

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  15. The product of any matrix by the scalar ......... Is the null matrix.

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  16. A matrix which is not a square matrix is called a..........matrix.

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  17. Matrix multiplication is distributive over matrix addition

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  18. If A is a symmetric matrix , then A^(3) is a ........ Matrix.

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  19. If A is a skew-symmetric matrix, then A^(2) is a .................

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  20. If A and B are square matrices of the same order, then (i) (AB)=.......

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