If A and B are two matrices such that AB = B and BA = A, A^2 + B^… - Vidyadip

MCQ

If $A$ and $B$ are two matrices such that $AB = B$ and $BA = A, A^2 + B^2$ is equal to$:$

A
$2AB$
B
$2BA$
✓
$A + B$
D
$AB$

✓

Answer

Correct option: C.

$A + B$

Given $AB = A$ and $BA = B,$ then
$\Rightarrow BAB = B^2$ and $ABA = A^2$
$\Rightarrow BA = B^2$ and $AB = A^2$
$\Rightarrow B = B^2$ and $A = A^2$
$\Rightarrow A^2 + B^2 = A + B$

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

Explore more

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

Similar questions

A die is thrown and a card is selected ar random from a deck pf $52$ playing cards. The probability of getting an even number of the die and a spade card is

The degree of the differntial equation $\Big(\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}\Big)^{2}=\Big(\frac{\text{dy}}{\text{dx}}\Big)=\text{y}^{3}$ is:

$\frac{1}{2}$
$2$
$3$
$4$

The differential equation of all parabolas whose axes are parallel to y-axis is:

$\frac{\text{dy}}{\text{dx}}=-\frac{\text{c}^2}{\text{x}^2}$
$\frac{\text{d}^2\text{x}}{\text{dy}^2}=\text{c}$
$\frac{\text{d}^3\text{y}}{\text{dx}^3}+\frac{\text{d}^2\text{x}}{\text{dy}^2}=0$
$\frac{\text{d}^2\text{y}}{\text{dx}^2}+2\frac{\text{dy}}{\text{dx}}=0$

If $A=\left[\begin{array}{ccc}1 & -2 & 4 \\ 2 & -1 & 3 \\ 4 & 2 & 0\end{array}\right]$ is the adjoint of a square matrix $B$, then $B^{-1}$ is equal to

If $\text{g}'(\text{x})=\int\text{x}^\text{x}\log_\text{e}(\text{ex})\text{dx}$ then $\text{g}(\pi)$ equals:

$\pi\log_\text{e}\pi$
$\pi^\pi\log_\text{e}(\text{e}\pi)$
$\pi^\pi\log_\text{e}(\pi)$
$\pi^\pi$

The solution of the differential equartion $y_1y_3 = y_2$ is$:$

If f(x) = |3 − x| + (3 + x), where (x) denotes the least integer greater than or equal to x, then f(x) is:

Continuous and differentiable at x = 3
Continuous but not differentiable at x = 3
Differentiable nut not continuous at x = 3
Neither differentiable nor continuous at x = 3

The angle of intersection of the curves $xy = a^2$ and $x^2 - y^2 = 2a^{2 }$ is:

The area bounded by the curve $\text{y}=\cos\text{x}$ in one are of the curve is where $=4\text{n}+1,\text{x}\in \text{integer:}$

$2\text{a}$
$\frac{1}{\text{a}} $
$\frac{2}{\text{a}}$
$2{\text{a}^2}$

If $A$ and $B$ are symmetric matrices of the same order, then