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Let A and B be invertible matrices then ...

Let A and B be invertible matrices then prove that `(AB)^-1=B^-1A^-1`.

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SRISIRI PUBLICATION-MATRICES-SHORT ANSWER TYPE QUESTIONS
  1. Show that |{:(a-b,b-c,c-a),(b-c,c-a,a-b),(c-a,a-b,b-c):}|=0

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  2. Show that |{:(1,a,a^2-bc),(1,b,b^2-ca),(1,c,c^2-ab):}|=0

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  3. Let A and B be invertible matrices then prove that (AB)^-1=B^-1A^-1.

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  4. Find the adjoint and the inverse of the matrix A=[{:(1,3,3),(1,4,3),(1...

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  5. Show that the matrix A=[{:(1,2,1),(3,2,3),(1,1,2):}] is non-singular a...

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  6. IF abc ne 0, find the inverse of [{:(a,0,0),(0,b,0),(0,0,c):}]

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  7. IF A=[{:(-1,-2,-2),(2,1,-2),(2,-2,1):}] then show that adj A=3A^T. Als...

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  8. IF A=[{:(3,-3,4),(2,-3,4),(0,-1,1):}] then show that A^-1=A^3.

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  9. IF 3A=[{:(1,2,2),(2,1,-2),(-2,2,-1):}] then show that A^-1=A'.

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  10. Find the rank of A=[{:(0,1,2),(1,2,3),(3,2,1):}] using elementary tran...

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  11. Find the rank of A=[{:(1,2,0,-1),(3,4,1,2),(-2,3,2,5):}] using element...

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  12. If A is a non-singular matrix then prove that A^(-1) = (adjA)/(|A|).

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  13. Show that |{:(a,b,c),(a^(2),b^(2),c^(2)),(a^(2),b^(3),c^(3)):}|=abc(a-...

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  14. Show that |{:(1,a^2,a^3),(1,b^2,b^3),(1,c^2,c^3):}| =(a-b)(b-c)(c-a)(a...

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  15. Show that |(a+b+2c,a,b),(c,b+c+2a,b),(c,a,c+a+2b)|=2(a+b+c)^(3).

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  16. Show that |{:(a-b-c," "2a," "2a),(" "2b,b-c-a," "2b),(" "2c," "2...

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  17. Show that |{:(a,b,c),(b,c,a),(c,a,b):}|=|{:(2bc-a^2,c^2,b^2),(c^2,2ac-...

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  18. Show that |{:(b+c,c+a,a+b),(c+a,a+b,b+c),(a+b,b+c,c+a):}|=2|{:(a,b,c),...

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  19. By Cramer's rule solve the system of equations 3x+4y+5z=18,2x+y+8z=13,...

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  20. Solve the equations 3x+4y+5z=18,2x+y+8z=13,5x-2y+7z=20 by matrix inver...

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