Download App

Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMatrices1 Mark
MCQ
Choose the correct answer from the given four options.
If $A$ and $B$ are matrices of same order, then $(AB\ ' – BA\ ')$ is a :
  • ✓
    Skew symmetric matrix.
  • B
    Null matrix.
  • C
    Symmetric matrix.
  • D
    Unit matrix.
✓

Answer

Correct option: A.
Skew symmetric matrix.
We have matrices $A$ and $B$ of same order.
Let $P = (AB\ ' - BA\ ')$
Then, $P\ ' = (AB\ ' - BA\ ')'$
$= (AB\ ')' - (BA\ ')'$
$= (B\ ')'(A)\ ' - (A\ ')'B\ ' $
$= BA\ ' - AB\ ' = -(AB\ ' - BA\ ') = -P$
Hence, $(AB\ ' - BA\ ')$ is a Skew symmetric matrix.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from Matrices→Matrices — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Let $m$ and $M$ be respectively the minimum and maximum values of

$\left|\begin{array}{ccc}\cos ^{2} x & 1+\sin ^{2} x & \sin 2 x \\ 1+\cos ^{2} x & \sin ^{2} x & \sin 2 x \\ \cos ^{2} x & \sin ^{2} x & 1+\sin 2 x\end{array}\right|$.

Then the ordered pair $( m , M )$ is equal to

→
If $\text{x}=\sin ^{ -1 }{ \text{K} },\text{y}=\cos ^{ -1 }\text{K}, -1\le \text{K}\le 1$, then the correct relationship is:
→
If $X$ has a binomial distribution, $B( n, p)$ with parameters $n$ and $p$ such that $P(X\, = 2)\, = P (X\, = 3)$, then $E(X)$, the mean of variable $X$, is
→
$A = \left[ {\begin{array}{*{20}{c}}4&6&{ - 1}\\3&0&2\\1&{ - 2}&5\end{array}} \right]$,$B = \left[ {\begin{array}{*{20}{c}}2&4\\0&1\\{ - 1}&2\end{array}} \right],\,\,C = \left[ {\begin{array}{*{20}{c}}3\\1\\2\end{array}} \right]$, then the expression which is not defined is
→
The solution of the differential equation $x\ dy + y\ dy = x^2y\  dy - y^2x\  dx$, is :
→
If $f(x)\, = \,2\,{\tan ^{ - 1}}\,x\, + \,{\sin ^{ - 1}}\,\left( {\frac{{2x}}{{1 + {x^2}}}} \right),x > 1\,$ then $f\,(5)$ is equal to
→
If $\triangle_1=\begin{vmatrix}1&1&1\\\text{a}&\text{b}&\text{c}\\\text{a}^2&\text{b}^2&\text{c}^2\end{vmatrix},\triangle_2=\begin{vmatrix}1&\text{bc}&\text{a}\\1&\text{ca}&\text{b}\\1&\text{ab}&\text{c}\end{vmatrix},$ then:
→
If $\int {}  e^u$ . $\sin 2x dx$ can be found in terms of known functions of $x$ then $u$ can be :
→
Choose the correct answer from the given four options.General solution of $\frac{\text{dy}}{\text{dx}}+\text{y}\tan\text{x}=\sec\text{x}$ is:
→
If $\int_{}^{} {f(x)\,dx} = x{e^{ - \log |x|}} + f(x),$ then $f(x)$ is
→