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If A is an invertible matrix of order 2,...

If A is an invertible matrix of order 2, then det `(A^(-1))` is equal to

A

det(A)

B

`(1)/(det(A))`

C

1

D

0

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to find the determinant of the inverse of a matrix \( A \) of order 2, given that \( A \) is an invertible matrix. ### Step-by-step Solution: 1. **Understanding the Determinant of an Inverse Matrix**: The determinant of the inverse of a matrix \( A \) is given by the formula: \[ \det(A^{-1}) = \frac{1}{\det(A)} \] This formula holds true for any invertible matrix, regardless of its order. 2. **Applying the Formula**: Since \( A \) is an invertible matrix of order 2, we can directly apply the formula: \[ \det(A^{-1}) = \frac{1}{\det(A)} \] 3. **Conclusion**: Therefore, the determinant of the inverse of matrix \( A \) is equal to the reciprocal of the determinant of \( A \): \[ \det(A^{-1}) = \frac{1}{\det(A)} \] ### Final Answer: \[ \det(A^{-1}) = \frac{1}{\det(A)} \]
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