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Question
If for any 2 x 2 square matrix A, `A("adj" "A") = [(8,0), (0,8)]`, then write the value of |A|
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Solution 1
Given A (adj A = `[(8,0),(0,8)]`
we know that A(adj A) = |A| - I
|A|.I = `8[(1,0),(0,1)]`
`=> |A| = 8`
Solution 2
It is given that
A(adj A) = `[(8,0),(0,8)]`
⇒ A(adj A) = `8[(1,0),(0,1)]`
⇒ A(adj A) = 8I2 .....(1)
We know that for any square matrix A of order 2, we have
A(adj A) = |A|I2 .....(2)
From (1) and (2), we have
|A|=8
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