Question

(e) If \(A\) and \(B\) are two invertible matrices of order \(n\), then:

• A. \((AB)^{-1} = B^{-1}A^{-1}\)
• B. \((AB)^{-1} = A^{-1}B^{-1}\)
• C. \((AB)^{-1} = A^{-1}B\)
• D. \((AB)^{-1} = AB^{-1}\)

Hint:

For invertible matrices, the product of inverses is taken in the reverse order of multiplication.

Answer 1

The Correct Option is A

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.