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(A^(3))^(-1)=(A^(-1))^(3), where A is a ...

`(A^(3))^(-1)=(A^(-1))^(3)`, where A is a square matrix and `|A|!=0`

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The correct Answer is:
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Since `(A^(n))^(-1)=(A^(-1))^(n)` where `n epsilonN`.
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NCERT EXEMPLAR-DETERMINANTS-Determinants
  1. If A is invertible matrix of order 3xx3, then |A^(-1)| is equal to…………

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  2. If x,y,zepsilonR then the value of |((2x^(x)+2^(-x))^(2),(2^(x)-2^(-x)...

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  3. If cos2theta=0, then |(0,costheta,sin theta),(cos theta, sin theta, 0)...

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  4. If is A is a matrix of order 3xx3, then (A^(2))^(-1) is equal to…………….

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  5. If A is a matrix of order 3xx3 then the number of minors in determinan...

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  6. The sum of products of elements of any row with the cofactors of corre...

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  7. If x=-9 is a root of |(x,3,7),(2,x,2),(7,6,x)|=0 then other two roots ...

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  8. |(0,xyz,x-z),(y-x,0,y-z),(z-x,z-y,0)| is equal to……………

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  9. If f(x)=|((1+x)^(17),(a+x)^(19),(1+x)^(23)),((a+x)^(23),(a+x)^(29),(1+...

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  10. (A^(3))^(-1)=(A^(-1))^(3), where A is a square matrix and |A|!=0

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  11. (aA)^(-1)=1/aA^(-1) where a is any real number and A is a square matri...

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  12. |A^(-1)|!=|A+^(-1), where A is a non singular matrix.

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  13. If A and B are matrices of order 3 and |A|=5,|B|=3, the |3AB|

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  14. If the value of a third order determinant is 12, then find the value o...

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  15. If a,b,c are in AP show that |[x+1,x+2,x+a],[x+2,x+3,x+b],[x+3,x+4,x+c...

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  16. |adjA|=|A|^(2) where A is a square matrix of order two.

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  17. Using properties of determinant. Prove that |[sinA,cosA,sinA+cosB],[si...

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  18. If the determinant |(x+a,p+u,l+f),(y+b,q+v,m+g),(z+c,r+w,n+h)| splits ...

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  19. If Delta=|(a,p,x),(b,q,y),(c,r,z)|=16 then Delta(1)=|(p+x,a+x,a+p),(q+...

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  20. The maximum value of |(1,1,1),(1,1+sintheta,1),(1,1,1+costheta)| is 1/...

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