Which of the following is an orthogonal matrix?

Important Questions on Matrices and Determinants

HARD

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-1>Q 32

If A is an orthogonal matrix & $\left|A\right|=-1$, then $A^T$is equal to-

MEDIUM

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-1>Q 33

Let $A=\left[\begin{array}{ccc}1& -1& 1\\ 2& 1& -3\\ 1& 1& 1\end{array}\right]$ and $10B=\left[\begin{array}{ccc}4& 2& 2\\ -5& 0& \alpha \\ 1& -2& 3\end{array}\right]$ .If $B$ is the inverse of $A$, then $\alpha$ is

EASY

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-1>Q 34

Let the matrix $A$ and $B$ be defined as $A=\left[\begin{array}{ll}3& 2\\ 2& 1\end{array}\right]$ and $B=\left[\begin{array}{ll}3& 1\\ 7& 3\end{array}\right]$ then the value of  $Det.\left(2A^9{B}^{-1}\right)$, is

HARD

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-1>Q 35

If $\left[\begin{array}{ll}2& 1\\ 7& 4\end{array}\right]A\left[\begin{array}{cc}-3& 2\\ 5& -3\end{array}\right]=\left[\begin{array}{ll}1& 0\\ 0& 1\end{array}\right]$, then matrix $A$ equals

MEDIUM

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-1>Q 36

If $A=\left[\begin{array}{ll}0& 5\\ 0& 0\end{array}\right]$ and $f\left(x\right)=1+x+x^2+\dots \dots +x^{16}$, then $\mathrm{f}\left(\mathrm{A}\right)=$

EASY

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-1>Q 37

If $M=\left[\begin{array}{ll}1& 2\\ 2& 3\end{array}\right]$ and $M^{\mathit{2}}\mathit{-}\lambda M\mathit{-}{I}_{\mathit{2}}\mathit{=}O$, then $\mathrm{\lambda }$ equals -

MEDIUM

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-1>Q 38

If $A=\left[\begin{array}{cc}1& -2\\ 3& 0\end{array}\right], B=\left[\begin{array}{cc}-1& 4\\ 2& 3\end{array}\right]$ and $ABC=\left[\begin{array}{ll}4& 8\\ 3& 7\end{array}\right]$, then $C$ equals -

MEDIUM

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-1>Q 39

If $P$ is a two-rowed matrix satisfying $P^T=P^{-1}$ , then $P$ can be -