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show that the matrix A=[(2,-2,-4),(-1,...

show that the matrix
`A=[(2,-2,-4),(-1,3,4),(1,-2,-3)]` is idempotent.

Text Solution

Verified by Experts

`A^(2)=A.A=[(2,-2,-4),(-1,3,4),(1,-2,-3)]xx[(2,-2,-4),(-1,3,4),(1,-2,-3)]`
`=[{:(2.2+(-2).(-1)(-4).1),((-1).2+3.(-1)+4.1),(12+(-2).(-1)+(-3).1),(2.(-2)+(-2).3+(-4).(-2)),((-1).(-2)+3.3+4.(-2)),(1.(-2)+(-2).3+(-3).(-2)),(2.(-4)+(-2).4+(-4).(-3)),((-1).(-4)+3.4.+4.(-3)),(1.(-4)+(-2).4+(-3).(-3)):}`
`[(2,-2,-4),(-1,3,4),(1,-2,-3)]=A`
Hence the matrix A is idempotent.
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