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

If A and B are symmetric matrices of the same order, then show that AB is symmetric if and only if A and B commute i.e AB = BA .

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PATHFINDER-MATRICES-QUESTION BANK
  1. if A=[[1,2,3],[3,-2,1],[4,2,1]] X=[(x),(y),(z)] and B=[(6),(2),(7)] ...

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  2. If A and B are tow matrices such that AB =O, can we deduce that eithe...

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  3. If A and B are symmetric matrices of the same order, then show that AB...

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  4. Find the values of x,y,z if , [[2x+y,x-y],[x-z,x+y+z]]=[[10,-1],[2,8]]

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  5. If A=[[2,-2],[4,2],[-5,1]]B=[[8,0],[4,-2],[3,6]]find the martrix X,suc...

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  6. Solve the matrix equation , [(x^2),(y^2)]-3 [(x),(2y)]=[(-2),(9)]

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  7. Assume that y, w and are matrices of order 3xxk,nxx3 and pxxk respecti...

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  8. If A is a squre matrix such that A^2 =A, then find the value of (1+A)^...

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  9. Find the inveres of [[1,2,4],[3,-19,7],[2,4,8]], if exists.

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  10. A and B are non-singular matrices of same order then show that adj(AB)...

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  11. If A = [[3,-5],[-4,2]],show that A^2-5A-14I =0.

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  12. If A =[[costheta,sintheta],[-sintheta,costheta]] then prove that A^n=[...

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  13. If A = [1,3,4],B=[[2,1],[3,7],[6,8]], C=[[3,4],[5,6],[1,0]] verify tha...

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  14. Express [[4,3,7],[6,5,-8],[1,2,6]] as the sum of a symmetric matrix an...

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  15. If B, C are a rowed squre matrices and if A=B+C, BC= CB, C^2=0, then s...

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  16. Let A = [[0,-tanalpha//2],[tanalpha//2,0]] and I, the indentity matrix...

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  17. Show that I+A =(I+A)*I

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  18. If A=[[2,-2],[4,2],[-5,1]]B=[[8,0],[4,-2],[3,6]]find the martrix X,suc...

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  19. If A=[[1,2],[-4,2]], then verify that A (adjA)=(adjA)A =abs(A)I2

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  20. A = [[3,-5],[-4,2]], verify that A^2-5A-14I=0, hence find A^(-1)

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