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A=[{:(a,b),(b,-a):}] and MA=A^(2m), m in...

`A=[{:(a,b),(b,-a):}]` and `MA=A^(2m)`, `m in N` for some matrix `M`, then which one of the following is correct ?

A

`(a^(2)+b^(2))^(m) I`

B

`(a^(2)+b^(2))^(m-1) A `

C

`-(a^(2)+b^(2))^(m-1)A `

D

`(a^(2)+b^(2))^(m) ` A

Text Solution

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The correct Answer is:
B
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MCGROW HILL PUBLICATION-MATRICES-SOLVED EXAMPLES ( LEVEL 1 ( Single Correct Answer Type Questions ) )
  1. The number of matrices A = [(a,b),(c,d)] ( where a,b,c,din R ) such...

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  2. Let A be a 3xx3 matrix with entries from the set of numbers, If the sy...

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  3. A=[{:(a,b),(b,-a):}] and MA=A^(2m), m in N for some matrix M, then whi...

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  4. Let A=[(a,b),(c,d)]be a 2 xx 2 matrix, where a, b, c, d take value 0 t...

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  5. Find the inverse of each of the matrices given below : Let D= "dia...

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  6. The inverse of a symmetric matrix ( if it exists ) is

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  7. Prove that inverse of a skew-symmetric matrix (if it exists) is skew-s...

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  8. The inverse of a skew symmetric matrix of odd order is a symmetric mat...

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  9. If A is an orthogonal matrix, then

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  10. If A = [(1,0,2),(5,1,x),(1,1,1)] is a singular matrix then x is equal ...

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  11. Find the value of x for which the matrix A=[(2//x,-1,2),(1,x,2x^(2)),(...

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  12. If a matrix A is such that 3A^3 +2A^2+5A+I= 0, then A^(-1) is equal to

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  13. If A=[(1,0),(1,1)] and I=[(1,0),(0,1)] then which one of the following...

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  14. If A, B, and C are three square matrices of the same order, then AB=AC...

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  15. If the product of the matrix B=[(2,6,4),(1,0,1),(-1,1,-1)] with a m...

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  16. If omega is a complex cube root of unity then the matrix A = [(1, omeg...

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  17. [{:(,0,1,2),(,1,2,3),(,3,a,1):}],=A^(-1)=[{:(,1//2,-1//2,1//2),(,-4,3,...

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  18. Let A=[[a,b],[c,d]] be a 2xx2 real matrix. If A-alphaI is invertible f...

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  19. If A =[(1,2),(3,4)] then A^(2)-5A equals

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  20. Solve system of linear equations, using matrix method, x y" "+" "2...

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