Question
If $\text{A} = \begin{bmatrix} \\cos\theta & \sin\theta & \\ -\sin\theta & \cos\theta & \\ \end{bmatrix}, $ then for any natural number n, find the value of Det $(A^{n}).$
✓
Answer
getting $|\text{A}| = 1$
$|\text{A}^{\text{n}}| = 1$
$|\text{A}^{\text{n}}| = 1$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Write the antiderivative of $\bigg(3\sqrt{\text{x}} + \frac{1}{\sqrt{\text{x}}}\bigg).$
→Classify the following as scalar and vector quantities:
Displacement.
Displacement.
Evaluate $\int \sqrt{1-\sin 2 x} d x$ :
→C and R represent set of complex numbers and real numbers. Show that $f: C \rightarrow R , f(z)=|z| \forall z \in C$ is neither one-one nor onto.
→What is the form of the differential equation $\frac{d y}{d x}-y \tan$ $x=e^x \sec x ?$
→$\int \sqrt{x^{2}-8 x+7} d x$ is equal to
→In triangle ABC, which of the following is not true:
$\int \frac{10 x^{9}+10^{x} \log _{e} 10 d x}{x^{10}+10^{x}}$, equals
→Find the following integrals in Exercises: $\int\frac{2-3\sin\text{x}}{\cos^2\text{x}}\text{ dx}$
→How many number of arbitrary constants in the general solution of a differential equation of fourth order.