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If A=[0 1 0 0] , prove that (a I+b A)^n=...

If `A=[0 1 0 0]` , prove that `(a I+b A)^n=a^n\ I+n a^(n-1)\ b A` where `I` is a unit matrix of order 2 and `n` is a positive integer.

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RD SHARMA ENGLISH-ALGEBRA OF MATRICES-All Questions
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  12. Compute the products A B and B A whichever exists in each of the fol...

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  18. If A=[(1,1),(0,1)] , show that A^2=[(1, 2),( 0, 1)] and A^3=[(1 ,3 ),(...

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  19. If A=[(ab ,b^2) ,(-a^2 ,-ab)] , show that A^2=O .

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  20. If A=[cos2thetasin2theta-sin2thetacos2theta] , find A^2 .

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