Question:
(e) If \(A\) and \(B\) are two invertible matrices of order \(n\), then:
(e) If \(A\) and \(B\) are two invertible matrices of order \(n\), then:
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For invertible matrices, the product of inverses is taken in the reverse order of multiplication.
Updated On: Mar 1, 2025
- \((AB)^{-1} = B^{-1}A^{-1}\)
- \((AB)^{-1} = A^{-1}B^{-1}\)
- \((AB)^{-1} = A^{-1}B\)
- \((AB)^{-1} = AB^{-1}\)
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The Correct Option is A
Solution and Explanation
The inverse of the product of two invertible matrices follows the rule:
\[
(AB)^{-1} = B^{-1}A^{-1}.
\]
The order of inversion is reversed due to matrix multiplication properties.
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