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For any 2xx2 matrix, if A\ (a d j\ A)=[[...

For any `2xx2` matrix, if `A\ (a d j\ A)=[[10 ,0 ],[0 ,10]]` , then `|A|` is equal to (a) 20 (b) 100 (c) 10 (d) 0

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RD SHARMA ENGLISH-ADJOINTS AND INVERSE OF MATRIX-All Questions
  1. If A= [ [1, 2] , [-1, 1]] , then det (a d j\ A)) is ?

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  2. If B is a non-singular matrix and A is a square matrix, then det (B^(-...

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  3. For any 2xx2 matrix, if A\ (a d j\ A)=[[10 ,0 ],[0 ,10]] , then |A| is...

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  4. If A^5=O such that A^n != I for 1 <= n <= 4, then (I - A)^-1 is equal ...

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  5. If A satisfies the equation x^3-5x^2+4x+lambda=0 , then A^(-1) exists ...

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  6. If for the matrix A ,\ A^3=I , then A^(-1)=(a)A^2 (b) A^3 (c) A (d) no...

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  7. If Aa n dB are two square matrices such that B=-A^(-1)B A ,t h e n(A+B...

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  8. If A=[(2 ,0 ,0),( 0 ,2 ,0),( 0 ,0 ,2)] , then A^5= (a) 5A (b) 10 A (c...

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  9. For non-singular square matrix A ,\ B\ a n d\ C of the same order th...

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  10. The matrix [(5 ,1 ,0), (3 ,-2 ,-4 ), (6 ,-1 ,-2b)] is a singular matri...

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  11. If d is the determinant of a square matrix A of order n , then the ...

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  12. If A is a matrix of order 3 and |A|=8 , then |a d j\ A|= (a) 1 (b)...

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  13. If A^2-A +I = 0, then the inverse of A is: (A) A+I (B) A (C) ...

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  14. If A and B are invertible matrices, which of the following statemen...

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  15. If A is a square matrix such that A^2 = I, then A^(-1) is equal to (i...

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  16. Let A=[(1, 2), (3,-5)] and B=[(1, 0), (0, 2)] and X be a matrix such t...

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  17. If A=[ (2 , 3) ,( 5 ,-2 )] , then find |A|

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  18. If A=1/3[(1,2,2),(2,1,-2),(x,2,y)] satisfies A^T A=I , then x+y= (a) ...

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  19. If A=[(1,0,1), (0,0,1),(a,b,2)] , then a I+b A+2A^2 equals (a) A (b) -...

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  20. If [(1,-tantheta),(tantheta,1)][(1,tantheta),(-tantheta,1)]^(-1)=[(a,-...

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