Advertisements
Advertisements
Question
If A is a non-singular square matrix such that \[A^{- 1} = \begin{bmatrix}5 & 3 \\ - 2 & - 1\end{bmatrix}\] , then find \[\left( A^T \right)^{- 1} .\]
Solution
For any invertible matrix A, \[( A^T )^{- 1} = ( A^{- 1} )^T\]
We have
\[ A^{- 1} = \begin{bmatrix}5 & 3 \\ - 2 & - 1\end{bmatrix}\]
\[ \Rightarrow ( A^T )^{- 1} = \begin{bmatrix}5 & - 2 \\ 3 & - 1\end{bmatrix}\]
APPEARS IN
RELATED QUESTIONS
Find λ and μ if
`(hati+3hatj+9k)xx(3hati-lambdahatj+muk)=0`
If A and B are square matrices of the same order such that |A| = 3 and AB = I, then write the value of |B|.
If A is a square matrix such that |A| = 2, write the value of |A AT|.
If A is a square matrix of order n × n such that \[|A| = \lambda\] , then write the value of |−A|.
If A and B are square matrices of order 2, then det (A + B) = 0 is possible only when
If A is a square matrix such that A (adj A) 5I, where I denotes the identity matrix of the same order. Then, find the value of |A|.
If A is a square matrix of order 3 such that |adj A| = 64, find |A|.
If A is a non-singular square matrix such that |A| = 10, find |A−1|.
If A is a square matrix of order 3 such that |A| = 2, then write the value of adj (adj A).
If A is a square matrix of order 3 such that adj (2A) = k adj (A), then write the value of k.
Let A be a 3 × 3 square matrix, such that A (adj A) = 2 I, where I is the identity matrix. Write the value of |adj A|.
If A is a square matrix such that \[A \left( adj A \right) = \begin{bmatrix}5 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 5\end{bmatrix}\] , then write the value of |adj A|.
Let A be a square matrix such that \[A^2 - A + I = O\], then write \[A^{- 1}\] interms of A.
If A and B are square matrices such that B = − A−1 BA, then (A + B)2 = ________ .
If \[A = \begin{bmatrix}2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2\end{bmatrix},\text{ then }A^5 =\] ____________ .
If A is a square matrix such that A2 = I, then A−1 is equal to _______ .
A is a square matrix with ∣A∣ = 4. then find the value of ∣A. (adj A)∣.
Let A = `[(1, "a" ("b + c"), "bc"),(1, "b" ("c + a"), "ca"),(1, "c" ("a + b"), "ab")],` then Det. A is ____________.
If A and B are square matrices of order 3, then ____________.
Given that A is a square matrix of order 3 and |A| = −4, then |adj A| is equal to:
Given that A = [aij] is a square matrix of order 3 × 3 and |A| = −7, then the value of `sum_("i" = 1)^3 "a"_("i"2)"A"_("i"2)`, where Aij denotes the cofactor of element aij is:
