If A is a square matrix such that A^2=A, then (1+A)^3-7 A is equa… - Vidyadip

MCQ

If $A$ is a square matrix such that $A^2=A$, then $(1+A)^3-7 A$ is equal to:

A
A
B
I - A
✓
I
D
3A

✓

Answer

Correct option: C.

I

Given: $A^2=A \ldots (i)$
Multiplying both sides by $A, A^3=A^2=A[$ From eq. (i) $] \ldots (ii)$
Also given $(I+A)^3-7 A=I^3+A^3+3 I^2 A+3 I A^2-7 A$
Putting $A^2=A\left[\right.$ from eq. (i)] and $A^3=A[$ from eq. $(ii)],$
$=I+A+3 I A+3 I A-7 A=I+A+3 A+3 A-7 A[\because I A=A]$
$=I+7 A-7 A=I$
Therefore, option $(C)$ is correct.

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

Given that the inverse trigonometric functions take principal values only. Then, the number of real values of $x$ which satisfy $\sin ^{-1}\left(\frac{3 x}{5}\right)+\sin ^{-1}\left(\frac{4 x}{5}\right)=\sin ^{-1} x$ is equal to:

The graph of the inequality $2 x+3 y>6$ is

$A$ = $f(x)$ = $\left[ {\begin{array}{*{20}{c}}
{\cos x}&{\sin x}&0 \\
{ - \sin x}&{\cos x}&0 \\
0&0&1
\end{array}} \right]$ . Then $A^{-1}$ is equal to

Which of the following six statements are true about the cubic polynomial

$P(x) = 2x^3 + x^2 + 3x - 2? $

$(i)$ It has exactly one positive real root.

$(ii)$ It has either one or three negative roots.

$(iii)$It has a root between $0$ and $1.$

$(iv)$ It must have exactly two real roots.

$(v)$ It has a negative root between $- 2$ and $-1.$

$(vi)$ It has no complex roots.

The velocity of a particle at time $t$ is given by the relation $v = 6t - {{{t^2}} \over 6}$. The distance traveled in $3$ seconds is, if $s = 0$ at $t = 0$

The system of equations $x + y + z = 6$, $x + 2y + 3z = 10,x + 2y + \lambda z = \mu $, has no solution for

The equations of tangent at those points where the curve $y = x^2 - 3x + 2$ meets x-axis are:

Choose the correct answer from given four options in each of the Exercise : There are two values of a which makes determinant $\begin{bmatrix}1 & -2 & 5 \\2 & \text{a} & 1\\0 & 4 & 2\text{a} \end{bmatrix} = 86,$ then sum of these number is :

If $A$ and $B$ are two matrices of same order, then $A + B$ is equal to :

If $ ABCDEF$ is regular hexagon, the length of whose side is a, then $\overrightarrow {AB} \,\,.\,\overrightarrow {AF} + \frac{1}{2}\,{\overrightarrow {BC} ^2} = $