If A = left[ {begin{array}{*{20}{c}}{cos θ }&{ - sin θ }{sin θ }&{cos θ }end{array}} rig

English

Gujarati

Hindi

3 and 4 .Determinants and Matrices

easy

If $A = \left[ {\begin{array}{*{20}{c}}{\cos \theta }&{ - \sin \theta }\\{\sin \theta }&{\cos \theta }\end{array}} \right]$, then which of the following statements is not correct

A

$A$ is orthogonal matrix

B

$A'$is orthogonal matrix

C

Determinant $A = 1$

D

$A$ is not invertible

Solution

(d) $|A|\,\, = 1 \ne 0,$ therefore $A$ is invertible.

Thus $ (d) $ is not correct.

Standard 12

Mathematics

Share

Similar Questions

If $A,B,C$are three $n \times n$ matrices, then $(ABC)' = $

normal

The matrix $A = \frac{1}{3}\left[ {\begin{array}{*{20}{c}}1&2&2\\2&1&{ – 2}\\{ – 2}&2&{ – 1}\end{array}} \right]$is

easy

If $A = \left( {\begin{array}{{20}{c}}1&{ – 2}&1\\2&1&3\end{array}} \right)$ and $B = \left( {\begin{array}{{20}{c}}2&1\\3&2\\1&1\end{array}} \right)$, then ${(AB)^T}$ is equal to

easy

If matrix $A = {\left[ {{a_{ij}}} \right]_{3 \times 3}} , B = {\left[ {{b_{ij}}} \right]_{3 \times 3}}$ , where $a_{ij} + a_{ji} = 0$ and $b_{ij} -b_{ji} = 0\, \forall\, i , j$ then $A^4B^3$ is

normal

How many $3 \times 3$ matrices $\mathrm{M}$ with entries from $\{0,1,2\}$ are there, for which the sum of the diagonal entries of $M^T M$ is $5$ ?

normal

(IIT-2017)