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if A and B are two matrices of order 3xx...

if `A` and `B` are two matrices of order `3xx3 `so that `AB=A` and `BA=B` then `(A+B)^7=`

A

`7(A+B)`

B

`7. I_(3xx3)`

C

`64 (A+B)`

D

`128 I`

Text Solution

Verified by Experts

The correct Answer is:
C
`AB=A, BA=B`
`ABA=A^(2)` or `A(BA)=A^(2)` or `A=A^(2)`
Similarly, `B^(2)=B`
`(A+B)^(2)=A^(2)+B^(2)+AB+BA`
`=A+B+A+B=2(A+B)`
`(A+B)^(3)=(A+B)^(2) (A+B)=2(A+B)^(2)=2^(2) (A+B)`
`implies (A+B)^(7)=2^(6)(A+B)=64 (A+B)`
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CENGAGE-MATRICES-Exercise (Comprehension)
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  2. Let a be a matrix of order 2xx2 such that A^(2)=O. tr (A) is equal t...

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  4. If A and B are two square matrices of order 3xx3 which satify AB=A and...

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  5. if A and B are two matrices of order 3xx3 so that AB=A and BA=B then (...

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  6. If A and B are two square matrices of order 3xx3 which satisfy AB=A an...

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  7. Consider an arbitarary 3xx3 non-singular matrix A[a("ij")]. A maxtrix ...

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  8. Let A=[a("ij")] be 3xx3 matrix and B=[b("ij")] be 3xx3 matrix such tha...

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  9. Let A=[(1,0,0),(1,0,1),(0,1,0)] satisfies A^(n)=A^(n-1)+A^(2)-I for n ...

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  10. Let A=[(1,0,0),(1,0,1),(0,1,0)] satisfies A^(n)=A^(n-1)+A^(2)-I for n ...

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  11. Let A=[(1,0,0),(1,0,1),(0,1,0)] satisfies A^(n)=A^(n-2)+A^(2)-I for n ...

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  12. Let for A=[(1,0,0),(2,1,0),(3,2,1)], there be three row matrices R(1),...

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  13. Let for A=[(1,0,0),(2,1,0),(3,2,1)], there be three row matrices R(1),...

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  14. A and B are square matrices such that det. (A)=1, B B^(T)=I, det (B) g...

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  15. A and B are square matrices such that det. (A)=1, B B^(T)=I, det (B) g...

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  16. Let A be an mxxn matrix. If there exists a matrix L of type nxxm such ...

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