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Without expanding, prove that |(a, b, c)...

Without expanding, prove that `|(a, b, c),( x, y, z),( p, q ,r)|=|(x, y, z),( p, q, r),( a, b, c)|=|(y, b, q),( x, a, p),( z, c, r)|`

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We have to prove that `|(a, b, c),( x, y, z),( p, q ,r)|=|(x, y, z),( p, q, r),( a, b, c)|=|(y, b, q),( x, a, p),( z, c, r)|`
Let `Delta =|(a, b, c),( x, y, z),( p, q ,r)|`
Now interchanged the rows `R_1` and `R_2` we get
`Delta =-|(x, y, z),( a, b, c),( p, q ,r)|`
Now interchanged the rows `R_2` and `R_3` we get
`Delta =-(-|(x, y, z),( p, q, r),( a, b ,c)|)`
`implies Delta =|(x, y, z),( p, q, r),( a, b ,c)|`
...
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