MCQ
If $A = \left( {\begin{array}{*{20}{c}}
2&{ - 1}\\
{ - 7}&4
\end{array}} \right)$ and $B = \left( {\begin{array}{*{20}{c}}
4&1\\
7&2
\end{array}} \right)$ then which of the following is correct
  • A
    $AA^T = I$
  • $(AB)^T = I$
  • C
    $BB^T = I$
  • D
    $AB \neq  BA$

Answer

Correct option: B.
$(AB)^T = I$
b

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

Similar questions

$\int_{}^{} {\left( {1 + x + \frac{{{x^2}}}{{2\;!}} + \frac{{{x^3}}}{{3\;!}} + ..........} \right)\;dx = } $
For $x \in R,x \ne 0$, if $y(x)$ is a differentiable function such that $x\int\limits_1^x {y\left( t \right)} dt = \left( {x + 1} \right)\int\limits_1^x {ty\left( t \right)} dt$ , then $y(x)$ equals (where $C$ is a constant)
Let $f'(x) > 0$ and $g'(x) < 0$ for all $x \in R$ then
$\int_{}^{} {\frac{{3\sin x + 2\cos x}}{{3\cos x + 2\sin x}}\;dx = } $
Choose the correct answer from the given four options.
Consider the non-empty set consisting of children in a family and a relation R defined as aRb if a is brother of b. Then R is:
  1. Symmetric but not transitive.
  2. Transitive but not symmetric.
  3. Neither symmetric nor transitive.
  4. Both symmetric and transitive.
Choose the correct answer from the given four options.

The solution of the differential equation $\frac{\text{dy}}{\text{dx}}+\frac{2\text{xy}}{1+\text{x}^2}=\frac{1}{(1+\text{x}^2)^2}$ is:

  1. $\text{y}(1+\text{x}^2)=\text{C}+\tan^{-1}\text{x}$

  2. $\frac{\text{y}}{1+\text{x}^2}=\text{C}+\tan^{-1}\text{x}$

  3. $\text{y}\log(1+\text{x}^2)=\text{C}+\tan^{-1}\text{x}$

  4. $\text{y}(1+\text{x}^2)=\text{C}+\sin^{-1}\text{x}$

If a curve the $y = f(x)$  passes through point $(1, -1)$ and  satisfies the differential equation $y\left( {1 + xy} \right)dx = xdy$ then $f\left( { - \frac{1}{2}} \right) = $ . . . . . 
Let $P=\left[a_{\|}\right]$be $a \times 3$ matrix and let $Q=\left[b_1\right]$, where $b_1=2^{1+j} a_{\|}$for $1 \leq i, j \leq 3$. If the determinant of $P$ is $2$ , then the determinant of the matrix $Q$ is
The value of f(0), so that the function $\text{f(x)}=\frac{(27-2\text{x})^\frac{1}{3}-3}{9-3(243+5\text{x})^\frac{1}{5}}$ is continuous, is given by:
  1. $\frac{2}{3}$
  2. 6
  3. 2
  4. 4
The function $f(x) = |x|$ at $x = 0$ is