If \( A \) is a nonsingular matrix such that \( A A^{T}=A^{T} A \) and \( B=A^{-1} A^{T} \), the....

Channel:
Subscribers:
447,000
Published on ● Video Link: https://www.youtube.com/watch?v=Dq2EecUYzFc



Duration: 2:56
0 views
0


If \( A \) is a nonsingular matrix such that \( A A^{T}=A^{T} A \)
\( \mathrm{P} \)
and \( B=A^{-1} A^{T} \), then matrix \( B \) is.
W
(1) Involuntary
(2) Orthogonal
(3) Idempotent
(4) None of these


📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live




Other Videos By PW Solutions


2024-01-21Let \( A \) be a matrix of order \( 2 \times 2 \) such that \( A^{2}=0 \). \( \operatorname{tr}(....
2024-01-21If \( \left(\begin{array}{cc}1 & -\tan \theta \\ \tan \theta & 1\end{array}\right)\left(\begin{a....
2024-01-21If \( Z \) is an idempotent matrix, then \( (I+Z)^{n} \)....
2024-01-21If \( \left[\begin{array}{cc}\cos \frac{2 \pi}{7} & -\sin \frac{2 \pi}{7} \\ \sin \frac{2 \pi}{7....
2024-01-21If \( A \) and \( B \) are squares matrices such that \( A^{2006}=O \) is \( A B=A+B \). then \(....
2024-01-21If \( A \) is a matrix such that \( A^{2}+A+2 I=O \), then which of the following is/are true?....
2024-01-21Let \( A=\left[\begin{array}{ll}0 & \alpha \\ 0 & 0\end{array}\right] \) and \( (A+I)^{50}-50 A=....
2024-01-21Matrix \( A \) such that \( A^{2}=2 A-I \), where \( I \) is the identity matrix, then for \( n ....
2024-01-21The number of solution of the matrix equation \( X^{2}=\left[\begin{array}{ll}1 & 1 \\ 2 & 3\end....
2024-01-21Consider three matrices \( A=\left[\begin{array}{ll}2 & 1 \\ 4 & 1\end{array}\right], B=\left[\b....
2024-01-21If \( A \) is a nonsingular matrix such that \( A A^{T}=A^{T} A \) and \( B=A^{-1} A^{T} \), the....
2024-01-21If \( A \) and \( B \) are square matrices of order \( n \), then \( A-\lambda I \) and \( B-\la....
2024-01-21If \( P \) is an orthogonal matrix and \( Q=P A P^{T} \) and \( \mathrm{x}=P^{T} Q^{1000} P \), ....
2024-01-21If \( A=\left[a_{i j}\right]_{4} \times 4 \), such that \( a_{i j}=\left\{\begin{array}{ll}2, & ....
2024-01-21If \( \mathrm{a}_{1}, \mathrm{a}_{2}, \mathrm{a}_{3}, 5,4, \mathrm{a}_{6}, \mathrm{a}_{7}, \math....
2024-01-21\( A \) is an involutory matrix given by \( A=\left[\begin{array}{ccc}0 & 1 & -1 \\ 4 & -3 & 4 \....
2024-01-21The system of equation \[ \begin{array}{l} x+3 y+2 z=6 \\ x+a y+2 z=7 \\ x+3 y+2 z=b \end{array}....
2024-01-21If \( n^{\text {th }} \)-order square matrix \( A \) is a orthogonal, then \( |\operatorname{adj....
2024-01-21Assertion (A): If every element of a third order determinant of value \( D \) is multiplied by 5....
2024-01-21Let \( D_{1}=\left|\begin{array}{ccc}a & b & a+b \\ c & d & c+d \\ a & b & a-b\end{array}\right|....
2024-01-21Let \( A \) be a \( 2 \times 2 \) matrix. Assertion (A): \( \operatorname{adj}(\operatorname{adj....