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True or False : If A is any square ma...

True or False :
If A is any square matrix, then det `(A^n) = (detA)^n` where n is any natural number.

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PRADEEP PUBLICATION-DETERMINANTS-EXERCISE
  1. True or False : If A and B are square matrices of the same order the...

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  2. True or False : If A and B are square marices of the same order, the...

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  3. True or False : If A is any square matrix, then det (A^n) = (detA)^...

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  4. True or False : If A and B are square matrices of the same order, th...

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  5. If the determiant |{:(x+a,p+u,l+f),(y+b,q+v,m+g),(z+c,r+w,n+h):}| spli...

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  6. True or False : Let A be a square matrix of order nge2 and B be the ...

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  7. True or False : The determinant of an identity matrix is always 1.

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  8. True or False : If A is a square matrix of order 1xx1 then adj A = O

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  9. Determinant of the 1xx1 matrix [-3] is

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  10. Determinant of the matrix A = [1,3,-5] is

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  11. The value of det [(cos theta, sintheta),(-sintheta, costheta)] is equa...

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  12. If A and B are invertible matrices of the same order, then (AB)^-1 is ...

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  13. A square matrix A invertible iff det A is equal to

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  14. If A is any of square matrix of order n, then A (adj A) is equal to

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  15. Prove that |(1,x,x^2),(1,y,y^2),(1,z,z^2)| = (x-y)(y-z)(z-x)

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  16. If A is a square matrix of order n, then det |lambdaA| is equal to (la...

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  17. If A is square matrix such that A^2 = I, then A ^-1 is equal to

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  18. If A is a square matrix of order 2, then det (adj A) is equal to

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  19. If A is a square matrix of order 2, then adj (adj A)

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  20. If A,B,C are three square matrices of the same order such that A= B +C...

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