JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(A=\left(\begin{array}{cc}1+ i & 1 \\ - i & 0\end{array}\right)\) where \(i =\sqrt{-1}\) Then, the number of elements in the set \(\left\{ n \in\{1,2, \ldots, 100\}: A ^{ n }= A \right\}\) is
- A \(255\)
- B \(25\)
- C \(75\)
- D \(80\)
Answer & Solution
Correct Answer
(B) \(25\)
Step-by-step Solution
Detailed explanation
\(A =\left[\begin{array}{cc}1+ i & 1 \\ - i & 0\end{array}\right]\) \(A ^{2}=\left[\begin{array}{cc}1+ i & 1 \\ - i & 0\end{array}\right]\left[\begin{array}{cc}1+ i & 1 \\ - i & 0\end{array}\right]\) \(A ^{2}=\left[\begin{array}{cc} i & 1+ i \\ - i +1 & - i \end{array}\right]\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- Let three real numbers \(a, b, c\) be in arithmetic progression and \(\mathrm{a}+1, \mathrm{~b}, \mathrm{c}+3\) be in geometric progression. If \(\mathrm{a}>10\) and the arithmetic mean of \(\mathrm{a}, \mathrm{b}\) and \(\mathrm{c}\) is \(8\) , then the cube of the geometric mean of \(a, b\) and \(c\) isJEE Mains 2024 Medium
- Let \(y=y(x)\) be the solution of the differential equations \(\frac{d y}{d x}+\frac{5}{x\left(x^5+1\right)} y=\frac{\left(x^5+1\right)^2}{x^7}, x > 0\). If \(y(1)=2\), then \(y(2)\) is equal toJEE Mains 2023 Hard
- If the vector \(\vec b = 3\hat j + 4\hat k\) is written as the sum of a vector \({\vec {b_1}}\) , parallel to \(\vec a = \hat i + \hat j\) and a vector \({\vec {b_2}}\) , perpendicular to \(\vec a\) , then \({\vec {b_1}} \times {\vec {b_2}}\) is equal toJEE Mains 2017 Hard
- Let for some function \(\mathrm{y}=f(x), \int_0^x t f(t) d t=x^2 f(x), x\gt0\) and \(f(2)=3\). Then \(f(6)\) is equal toJEE Mains 2025 Medium
- The area (in sq, units) of the quadrilateral formed by the tangents at the end points of the latera recta to the ellipse \(\frac{{{x^2}}}{9} + \frac{{{y^2}}}{5} = 1\) is :JEE Mains 2015 Hard
- The value of the integral \(\int \frac{\sin \theta \cdot \sin 2 \theta\left(\sin ^{6} \theta+\sin ^{4} \theta+\sin ^{2} \theta\right) \sqrt{2 \sin ^{4} \theta+3 \sin ^{2} \theta+6}}{1-\cos 2 \theta} d \theta\) is (where \(c\) is a constant of integration)JEE Mains 2021 Hard
More PYQs from JEE Mains
- The inverse function of \(f(\mathrm{x})=\frac{8^{2 \mathrm{x}}-8^{-2 \mathrm{x}}}{8^{2 \mathrm{x}}+8^{-2 \mathrm{x}}}, \mathrm{x} \in(-1,1),\) isJEE Mains 2020 Hard
- The area of the region (in sq. units), in the first quadrant bounded by the parabola \(y = 9x^2\) and the lines \(x = 0,y = 1\) and \(y = 4,\) isJEE Mains 2013 Hard
- If the system of linear equations \(x_1 + 2x_2 + 3x_3 = 6\) ; \(x_1 + 3x_2 + 5x_3 = 9\) ; \(2x_1 + 5x_2 + ax_3 = b\) is consistent and has infinite number of solutions, thenJEE Mains 2013 Hard
- A point on the straight line, \(3x + 5y = 15\) which is equidistant from the coordinate, axes will lie only inJEE Mains 2019 Hard
- Suppose Anil's mother wants to give \(5\) whole fruits to Anil from a basket of \(7\) red apples, \(5\) white apples and \(8\) oranges. If in the selected \(5\) fruits, at least \(2\) orange, at least one red apple and at least one white apple must be given, then the number of ways, Anil's mother can offer \(5\) fruits to Anil is \(........\)JEE Mains 2023 Hard
- Let \(H: \dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1\) be a hyperbola such that the distance between its foci is \(6\) and the distance between its directrices is \(\dfrac{8}{3}\). If the line \(x=\alpha\) intersects the hyperbola \(H\) at the points \(A\) and \(B\) such that the area of the triangle \(AOB\) is \(4\sqrt{15}\), where \(O\) is the origin, then \(\alpha^2\) equalsJEE Mains 2026 Medium