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If A=[[3,-5],[-4,2]], find A^2-5A-14I....

If `A=[[3,-5],[-4,2]]`, find `A^2-5A-14I`.

Text Solution

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`A^2=A*A=[[3,-5],[-4,2]][[3,-5],[-4,2]]`
`=[[29,-25],[-30,24]]`
`A^2-5A-14I`
`=[[29,-25],[-2-,24]]-[[15,-25],[-20,10]]-[[14,0],[0,14]]`
`=[[0,0],[0,0]]`
Zero matrix.
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