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Let A=[(0,1),(0,0)], show that (aI+bA)^(...

Let `A=[(0,1),(0,0)]`, show that `(aI+bA)^(n)=a^(n)I+na^(n-1)bA`, where I is the identity matrix of order 2 and `n in N`.

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Knowledge Check

  • Let n ge 2 be an integer, A=({:(cos((2pi)/(n)),sin((2pi)/(n)),0),(sin((2pi)/(n)),cos((2pi)/(n)),0),(0,0,1):}) and I is the idnetity matrix of order 3. Then

    A
    `A^(n)=I " and " A^(n-1) ne I`
    B
    `A^(m) ne I` for any positive integer m
    C
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    D
    `A^(m)=0` for a positive integer m

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