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Question
If A is an invertible matrix of order 2, then det (A−1) is equal to ______.
Options
det (A)
`1/det (A)`
1
0
Solution
If A is an invertible matrix of order 2, then det (A−1) is equal to `underline(1/det (A))`.
Explanation:
`because` A invertible matrix `=> abs "A" ne 0`
`therefore "AA"^-1 = "I"` and `abs ("AA"^-1) = abs "I" = 1`
`=> abs "A" abs ("A"^-1) = 1`
`=> abs ("A"^-1) = 1/abs "A"`
`=> det ("A"^-1) = 1/det("A")`
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