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प्रश्न
Find the inverse of the matrices (if it exists).
`[(2,-2),(4,3)]`
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उत्तर
Let A = `[(2,-2),(4,3)]`
Then, |A| = `|(2,-2),(4,3)|`
= 6 + 8
= 14 ≠ 0
So, A is a non-singular matrix and therefore it is invertible. Let Cij be the cofactor of aij in A.
Then, the cofactors of elements of A are given by,
C11 = (−1)1+1 (3) = 3
C12 = (−1)1+2 (4) = (−4)
C21 = (−1)2+1 (−2) = 2
C22 = (−1)2+2 (2) = 2
∴ Adj A = `[(3,-4),(2,2)]^' = [(3,2),(-4,2)]`
Hence, A−1 = `1/|A| ("Adj A")`
= `1/14 [(3,2),(-4,2)]`
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