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If I = [(1,0),(0,1)] and E = [(0,1),(0,0...

If `I = [(1,0),(0,1)] and E = [(0,1),(0,0)]` then show that `(aI + bE)^(3) = a^(3)I+3a^(2)bE` where I is identify matrix of order 2.

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Explore conceptually related problems

If I=[{:(1,0),(0,1):}] and E=[{:(0,1),(0,0):}] , show that (aI + bE)^(3) =a^(3)I + 3a^(2)bE . Where I is unit matrix of order 2.

if A = [(I,0)(0,-i)] then show that A^(2) = -1 (i^(2)=-1) .

Knowledge Check

  • If A=[(0,-1),(1,0)],B=[(0,i),(i,0)] then

    A
    `A^(2)=B^(2)=I`
    B
    `A^(2)=B^(2)=-I`
    C
    `A^(2)=I,B^(2)=-I`
    D
    `A^(2)=-I,B^(2)=I`

  • If A=[(i,0),(0,-i)],B=[(0,-1),(1,0)],C=[(0,i),(i,0)] then

    A
    `AB=-BA=-I`
    B
    `AB=-BA=O`
    C
    `AB=-BA=I`
    D
    none

  • If A=[(i,0),(0,-i)],B=[(0,-1),(1,0)],C=[(0,i),(i,0)] then

    A
    `A^(2)=B^(2)=C^(2)=-I`
    B
    `A^(2)=B^(2)=C^(2)=O`
    C
    `A^(2)=B^(2)=C^(2)=I`
    D
    none

    • Similar Questions

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    If A=[{:(1,-2,1),(0,1,-1),(3,-1,1):}] then show that A^3-3A^2-A-3I=O , where I is unit matrix of order 3

    If A= [(i,0),(0,-i)] , then show that A^(2)= -I, (i^(2)= -1)

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