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Let I denote the 3xx3 and P be a matrix ...

Let I denote the `3xx3` and P be a matrix obtained by rearranging the columns of I. Then

A

1) there are six distinct choices for P and det (P) = 1

B

2) there are six distinct choices for P and det(P)=`+-1`

C

3) there are more than one choices for P and some of them are not invertible.

D

4) there are more than one choices for P and `P^-1` = I in each choice.

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MODERN PUBLICATION-DETERMINANTS-EXERCISE
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  4. If A is matrix of order 3,such that A(adjA)=10I. Then |adjA|=

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  5. Without expanding the determinant at any stage, prove that {:|(x+1,x+2...

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  9. Let M and N be two 3xx3 non-singular skew-=symmetric matrices such t...

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  11. The number of values of k, for which the system of equations (k""+""...

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  12. If P=[[1,alpha,3],[1,3,3],[2,4,4]] is the adjoint of a 3xx3 matrix A a...

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  13. If {:|(x,x),(1,x)| = |(3,4),(1,2)|. Write the positive value of 'x'.

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  14. If A is a square matrix of order 3 and |3A| = k|A|, then write the val...

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  15. If A is a square matrix order 3 such that |adjA|=225, find |A'|.

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  16. Prove 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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  17. Using the properties of determinant, show that :|[a^2+1,ab,ac],[ab,b^2...

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  18. Using Cofactors of elements of third column, evaluate triangle - |[1,x...

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  19. Find the value of k’ if the area of the triangle is 4 sq. units and ve...

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