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Let S be the set of all 2xx2 real matric...

Let S be the set of all `2xx2` real matrices A `= [(a,b),(c,d)]` such that a+d=3 and A=`A^(2) -3A` . Then

A

S contains infinite number of elements

B

S=Q

C

S contains exactly two elements

D

S contains exactly `2^(4)` elements

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The correct Answer is:
B
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MCGROW HILL PUBLICATION-MATRICES-EXERCISE ( LEVEL -1) (Single Correct Answer Type Questions)
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  3. Let A = (a(ij)(3xx2) be a 3xx2 matrix with real entries and B = AA. T...

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  6. If A is both diagonal and skew - symmetric then

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  7. If A^(2) - 3A +2I =0 then A^(-1) equals

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  8. If A is a square matrix of order 3 such that A^(2) = 2A then |A|^(2) ...

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  10. If A = (a(ij))(3xx3) where a(ij) = cos (i+j) then

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  11. If A = (a(ij))(3xx) is a matrix satrisfying the equation x^(3) -3x+1 =...

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  12. Let A and B be square matrices of the same order. Does (A+B)^2=A^2+...

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  13. If [(I,0),(3,-i)]+X = [(I,2),(3,4+i)] -X then X is equal to

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  14. If A = [(0,-i),(i,0)] B = [(1,0),(0,-1)] then A B+ BA is

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  15. A =[(1,2,3),(1,2,3),(-1,-2,-3)] then A is a nilpotent matrix of index

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  16. If A is a 2xx2 unitary matrix then |A| is equal to

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  17. If A= (1)/(2) ((-1,-sqrt(3)),(sqrt(3),-1)) then A^(-1)- A^(2) is equal...

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  19. If A , B and C are three square matrices of the same size such that B ...

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  20. If X is a 2 xx 3 matrix such that |X' X|!=0 and A = I2 - X(X' X)^(-1) ...

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