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If A and B are square matrices of the...

If `A` and `B` are square matrices of the same order such that `A B=B A` , then show that `(A+B)^2=A^2+2A B+B^2` .

A

`AB = I`

B

`BA=I`

C

`AB=BA`

D

none of these

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The correct Answer is:
C
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OBJECTIVE RD SHARMA ENGLISH-MATRICES-Exercise
  1. If A = [a(ij)] is a skew-symmetric matrix of order n, then a(ij)=

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  2. If A and B are symmetric matrices of the same order, write whether ...

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  3. If A and B are square matrices of the same order such that A B=B A ...

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  4. The trace of the matrix A=[1-5 7 0 7 9 11 8 9] is (a) 17 (b) 25 ...

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  5. If A is a skew- symmetric matrix, then trace of A is: 1.) 1 2.) -...

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  6. If {:A=[(1,x),(x^7,4y)],B=[(-3,1),(1,0)]and adjA+B=[(1,0),(0,1)]:}, th...

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  7. If A is a square matrix of order n xx n and k is a scalar, then adj (k...

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  8. If A is a singular amtrix, then adj A is

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  9. If A is a non singular square matrix; then adj(adjA) = |A|^(n-2) A

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  10. If A is a singular amtrix, then adj A is

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  11. If A=[(cosx,sinx),(-sinx,cosx)] and A.(adjA)=k[(1,0),(0,1)] then the v...

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  12. If A=[[1,1],[1,1]] ,prove that A^n=[[2^(n-1),2^(n-1)],[2^(n-1),2^(n-1)...

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  13. If A=[{:(a,b),(b,a):}] and A^(2)=[{:(alpha, beta),(beta, alpha):}] the...

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  14. If A is an invertible square matrix; then adj A^T = (adjA)^T

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  15. If A=[[1,3] , [3,4]] and A^2-kA-5I2=0 then k=

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  16. If A=[a(ij)] is a scalar matrix, then trace of A is

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  17. If A=[a(i j)] is a scalar matrix of order nxxn such that a(i i)=k f...

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  18. If A=[a(i j)] is a scalar matrix of order nxxn such that a(i i)=k f...

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  19. If A=[a(ij)] is a scalar matrix of order nxxn and k is a scalar, then ...

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  20. If f(alpha)=[[cosalpha,-sinalpha,0],[sinalpha,cosalpha,0],[ 0, 0, 1]],...

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