If A = [[x,4],[y,8]]

determine the values of x and y for which A^2=A

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`A=[[x,4],[y,8]]`

`A.A=[[x,4],[y,8]][[x,4],[y,8]]=[[x^2+4y,4x+32],[xy+8y,4y+64]]`

`` By given condition

`[[x^2+4y,4x+32],[xy+8y,4y+64]]=[[x,4],[y,8]]`

comparing the elements of the matrices, we have

`4x+32=4`

`x=-7`

`4y+64=8`

`y=-14`

So ans. x=-7,y=-14

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