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:
Show Hint
For invertible matrices, the product of inverses is taken in the reverse order of multiplication.
Updated On: Mar 1, 2025
- \((AB)^{-1} = B^{-1}A^{-1}\)
- \((AB)^{-1} = A^{-1}B^{-1}\)
- \((AB)^{-1} = A^{-1}B\)
- \((AB)^{-1} = AB^{-1}\)
Hide Solution
Verified By Collegedunia
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.
Was this answer helpful?
0
0
Top Questions on Vector Algebra
- Assertion (A): If $| \mathbf{a} \times \mathbf{b} |^2 + | \mathbf{a} \cdot \mathbf{b} |^2 = 256$ and $| \mathbf{b} | = 8$, then $| \mathbf{a} | = 2$.
Reason (R): $\sin^2 \theta + \cos^2 \theta = 1$ and $| \mathbf{a} \times \mathbf{b} | = | \mathbf{a} | | \mathbf{b} | \sin \theta$ and $ \mathbf{a} \cdot \mathbf{b} = | \mathbf{a} | | \mathbf{b} | \cos \theta$.- CBSE CLASS XII - 2025
- Mathematics
- Vector Algebra
- Find the angle between the vectors \( -2\hat{i} + \hat{j} + 3\hat{k} \) and \( 3\hat{i} - 2\hat{j} + \hat{k} \).
- UP Board XII - 2025
- Mathematics
- Vector Algebra
- Find the projection of the vector \(\vec{a} = 2\hat{i} + 3\hat{j} + 2\hat{k}\) on the vector \(\vec{b} = \hat{i} + 2\hat{j} + \hat{k}\).
- UP Board XII - 2025
- Mathematics
- Vector Algebra
- Find the unit vector perpendicular to each of the vectors \( (\vec{a} + \vec{b}) \) and \( (\vec{a} - \vec{b}) \) where \( \vec{a} = \hat{i} + \hat{j} + \hat{k} \) and \( \vec{b} = \hat{i} + 2\hat{j} + 3\hat{k} \).
- UP Board XII - 2025
- Mathematics
- Vector Algebra
- If \(|\vec{a}| = 5\), \(|\vec{b}| = 13\), and \(|\vec{a} \times \vec{b}| = 25\), then \(|\vec{a} \cdot \vec{b}|\) is equal to ........
View More Questions
Questions Asked in UP Board XII exam
- Answer the following questions in about 40 words each:
(b) What did Roosevelt say about fear in the lesson 'Deep Water'?- UP Board XII - 2025
- Literature
- The antonym of 'ancient' is
- UP Board XII - 2025
- Antonyms
- Change any one of the following into indirect speech:
(i) She said, "Brother, I shall give you my watch."- UP Board XII - 2025
- Direct And Indirect Speech
- If the sequence of one strand of DNA is written as follows: 5' - ATGC ATGC ATGC ATGC ATGC - 3', write down the sequence of the complementary strand in 3' → 5' direction.
- UP Board XII - 2025
- Genetics
- Write a note on Intra-Uterine Devices (IUD’s) and their applications.
- UP Board XII - 2025
- Reproductive Biology
View More Questions