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If A and B are two square matrices of or...

If A and B are two square matrices of order `3xx3` which satify `AB=A` and `BA=B`, then
Which of the following is true ?

A

If matrix A is singular, then matrix B is nonsingular.

B

If matrix A is nonsingular, then materix B is singular.

C

If matrix A is singular, then matrix B is also singular.

D

Cannot say anything.

Text Solution

Verified by Experts

The correct Answer is:
C
`AB=A implies |AB|=|A|` (1)
`implies |A|=0` or `|B|=1`
`BA=B implies |BA|=|B|` (2)
`implies |A|=1` or `|B|=0`
If `|A|=0`, then from Eq. (2) `|B|=0`
If `|B|=0`, then from Eq. (1), `|A|=0`
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CENGAGE-MATRICES-Exercise (Comprehension)
  1. Let a be a matrix of order 2xx2 such that A^(2)=O. A^(2)-(a+d)A+(ad-...

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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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  3. Let a be a matrix of order 2xx2 such that A^(2)=O. (I+A)^(100) =

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

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

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