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Let a be a matrix of order 2xx2 such tha...

Let a be a matrix of order `2xx2` such that `A^(2)=O`.
`A^(2)-(a+d)A+(ad-bc)I` is equal to

A

`I`

B

`O`

C

`-I`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Let
`A=[(a,b),(c,d)]`
`implies A^(2)-(a+d)A+(ad-bc)I`
`=[(a,b),(c,d)][(a,b),(c,d)]-(a+d)[(a,b),(c,d)]+(ad-bc)[(1,0),(0,1)]`
`=[(a^(2)+bc,ab+bd),(ac+cd,bc+d^(2))]-[(a^(2)+ad,ab+bd),(ac+cd,bc+d^(2))]+[(a^(2)+ad,ab+bd),(ac+cd,ad+d^(2))]`
`=O`
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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 satify AB=A and...

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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-1)+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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