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प्रश्न
Verify A(adj A) = (adj A)A = |A|I.
`[(2,3),(-4,-6)]`
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उत्तर
Let, A = `[(2,3),(-4,-6)]`
|A| = −12 + 12
|A| = 0
A11 = (−1)1+1 M11 = −6
A12 = (−1)1+2 M12 = −(−4) = 4
A21 = (−1)2+1 M21 = −3
A22 = (−1)2+2 M22 = 2
Adj A = `[(-6,-3),(4,2)]`
L.H.S. = A(adj A) = `[(2,3),(-4,-6)] [(-6,-3),(4,2)]`
= `[(2 xx (- 6) + 3 xx 4, 2 xx (-3) + 3 xx 2),(- 4 xx (- 6) + (- 6) xx 4, - 4 xx (- 3) + (- 6) xx 2)]`
= `[(-12 + 12, -6 + 6),(24 - 24, 12 - 12)]`
= `[(0,0),(0,0)]`
R.H.S. = (adj A)A `= [(-6,-3),(4,2)][(2,3),(-4,-6)]`
= `[(-12 + 12,-18 + 18),(8 - 8, 12 - 12)]`
= `[(0,0),(0,0)]`
|A| · I = `0 · [(1,0),(0,1)]`
= `[(0,0),(0,0)]`
Hence, A(adj A) = (adj A)A = |A| · I
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