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If A = [[0,1],[0,0]], I is the unit null...

If `A = [[0,1],[0,0]]`, I is the unit null matrix of order 2 and a,b are arbitrary constants, then `(aI+bA)^2` is equal to

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`A = [[0,1],[0,0]]`
`I = [[1,0],[0,1]]`
`:. aI +bA = a[[1,0],[0,1]] + b[[0,1],[0,0]] =[[a,0],[0,a]]+ [[0,b],[0,0]] = [[a,b],[0,a]]`
`:. (aI+bA)^2 = [[a,b],[0,a]][[a,b],[0,a]] = [[a^2,ab+ab],[0,a^2]]`
`= [[a^2,2ab],[0,a^2]]`
`=[[a^2,0],[0,a^2]]+[[0,2ab],[0,0]]`
. `=a^2[[1,0],[0,1]]+2ab[[0,1],[0,0]]`
`= a^2I+2abA`
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