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Let A be a 2xx2 matrix Statement -1 ad...

Let A be a `2xx2` matrix
Statement -1 adj `(adjA)=A`
Statement-2 `abs(adjA) = abs(A)`

A

Statement -1 is true, Statement-2 is true, Statement-2 is a
correct explanation for Statement-1

B

Statement -1 is true, Statement - 2 is true, Statement -2 is not
a correct explanation for Statement-1

C

Statement-1 is true, Statement-2 is false

D

Statement-1 is false, Statement-2 is true

Text Solution

Verified by Experts

The correct Answer is:
B
`abs(adjA) = abs(A)^(n-1) = abs(A)^(2-1)=abs(A)`
`adj ("adj A")=abs(A)^(n-2)A`
`=abs(A)^(2-2) A= abs(A)^(0) A = A`
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ARIHANT MATHS-MATRICES -Exercise (Questions Asked In Previous 13 Years Exam)
  1. Let A be the set of all 3xx3 symmetric matrices all of whose either 0 ...

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  2. Let A be the set of all 3xx3 symmetric matrices all of whose either 0 ...

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  3. Let A be a 2xx2 matrix Statement -1 adj (adjA)=A Statement-2 abs(a...

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  4. The number of 3xx3 matrices A whose entries are either 0or1 and for wh...

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  5. Let p be an odd prime number and Tp be the following set of 2 x 2 ma...

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  6. Let p be an odd prime number and Tp, be the following set of 2 xx 2 ma...

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  7. Let p be an odd prime number and Tp be the following set of 2 x 2 ma...

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  8. Let K be a positive real number and A=[2k-1 2sqrt(k)2sqrt(k)2sqrt(k)1-...

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  9. The number of 3 3 non-singular matrices, with four entries as 1 and ...

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  10. Let A be a 2 xx 2 matrix with non-zero entries and let A^2=I, where i ...

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  11. Let Ma n dN be two 3xx3 non singular skew-symmetric matrices such that...

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  12. Let a,b, and c be three real numbers satistying [a,b,c][(1,9,7),(8,2,7...

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  13. Let a,b, and c be three real numbers satistying [a,b,c][(1,9,7),(8,2,7...

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  14. Let a,b, and c be three real numbers satistying [a,b,c][(1,9,7),(8,2,7...

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  15. Let omega!=1 be cube root of unity and S be the set of all non-singula...

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  16. Let M be a 3xx3 matrix satisfying M[0 1 0]=M[1-1 0]=[1 1-1],a n dM[1 1...

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  17. Let A and B are symmetric matrices of order 3. Statement -1 A (BA) a...

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  18. Let P = [a(ij)] " be a " 3 xx 3 matrix and let Q = [b(ij)], " where " ...

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  19. If P is a 3xx3 matrix such that P^T = 2P+I, where P^T is the transpose...

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  20. If the adjoint of a 3 3 matrix P is 1 4 4 2 1 7 1 1 3 , then the po...

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