Download App

3 and 4 . determinant and metrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths3 and 4 . determinant and metrices1 Mark
MCQ
If $A$ is square matrix such that $A^{2}=A$, then $(1+A)^{3}-7 A$ is equal to
  • A
    $A$
  • B
    $I-A$
  • C
    $3A$
  • ✓
    $I$
✓

Answer

Correct option: D.
$I$
d
$(I+A)^{3}-7 A=I^{3}+A^{3}+3 I^{2} A+3 A^{2} I-7 A$

$=I+A^{3}+3 A+3 A^{2}-7 A$

$=I+A^{2} \cdot A+3 A+3 A-7 A$                       $\left[A^{2}=A\right]$

$=I+A \cdot A-A$

$=I+A^{2}-A$

$=I+A-A$

$=I$

$\therefore(I+A)^{3}-7 A=I$

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 3 and 4 . determinant and metrices→3 and 4 . determinant and metrices — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If $x + \frac{1}{x} = 2$, the principal value of ${\sin ^{ - 1}}$ $x$ is
→
If the vectors $6i - 2j + 3k,\,\,2i + 3j - 6k$ and $3i + 6j - 2k$ form a triangle, then it is
→
If $f(x)=\left\{\begin{array}{l}x, \text { if } x \leq 1 \\ 7, \text { if } x>1\end{array}\right.$, then
→
If $\text{I}=\begin{bmatrix}1&0\\0&1\end{bmatrix},\text{J}=\begin{bmatrix}0&1\\-1&0\end{bmatrix}$ and $\text{B}=\begin{bmatrix}\cos\theta&\sin\theta\\-\sin\theta&\cos\theta\end{bmatrix},$ then B equals:
  1. $\text{I}\cos\theta+\text{J}\sin\theta$
  2. $\text{I}\sin\theta+\text{J}\cos\theta$
  3. $\text{I}\cos\theta-\text{J}\sin\theta$
  4. $-\text{I}\cos\theta+\text{J}\sin\theta$
→
How many lines through the origin in make equal angles with the coordinate axis:
→
Range of the function

$f(x) = \sqrt {\left| {{{\sin }^{ - 1}}\left| {\sin x} \right|} \right| - {{\cos }^{ - 1}}\left| {\cos x} \right|} $ is

→
Let f(x) = (x + |x|) |x|. Then, for all x:
  1. f is continuous.
  2. f is differentiable for some x
  3. f' is continuous.
  4. f'' is continuous.
→
The relation R = {(1, 1), (2, 2), (3, 3)} on the set {1, 2, 3} is:
  1. Symmetric only.
  2. Reflexive only.
  3. An equivalence relation.
  4. Transitive only.
→
Area bounded between the curve x2 = y and the line y = 4x is:
  1. $\frac{32}{3}\text{sq}\text{ unit}$
  2. $\frac{1}{3}\text{sq}\text{ unit}$
  3. $\frac{8}{3}\text{sq}\text{ unit}$
  4. $\frac{16}{3}\text{sq}\text{ unit}$
→
Find the determinant of the matrix $\text{A}=\begin{bmatrix}9&8\\7&6\end{bmatrix}$ is:
  1. -1
  2. 1
  3. 2
  4. -2
→