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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
`(A+I)^(5)` is equal to (where I is idensity matric)

A

`I+60A`

B

`I+16A`

C

`I+31A`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`(A+I)^(5)=I+5A+10A^(2)+10A^(3)+5A^(4)+A^(5)`
`=I+5A+10A+10A+5A+A`
`( :' A^(2)=Aimplies A^(3)=A^(4)=A^(5)= =A)`
`=I +31 A`
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CENGAGE PUBLICATION-MATRICES-All Questions
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  2. if A and B are two matrices of order 3xx3 so that AB=A and BA=B then (...

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

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

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

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  6. 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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  7. 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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  8. 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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  9. Let for A=[(1,0,0),(2,1,0),(3,2,1)], there be three row matrices R(1),...

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

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

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

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

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

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  19. Consider a matrix A=[a("ij")] of order 3xx3 such that a("ij")=(k)^(i+j...

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