If A= i&0 0&i , write A2. - Vidyadip

Question

If $\text{A}=\begin{bmatrix}\text{i}&0\\0&\text{i}\end{bmatrix},$ write A².

✓

Answer

Given: $\text{A}=\begin{bmatrix}\text{i}&0\\0&\text{i}\end{bmatrix}$
$\text{A}^2=\text{AA}$
$\Rightarrow\text{A}^2=\begin{bmatrix}\text{i}&0\\0&\text{i}\end{bmatrix}\begin{bmatrix}\text{i}&0\\0&\text{i}\end{bmatrix}$
$\Rightarrow\text{A}^2=\begin{bmatrix}\text{i}^2+0&0+0\\0+0&0+\text{i}^2\end{bmatrix}$
$\Rightarrow\text{A}^2=\begin{bmatrix}\text{i}^2&0\\0&\text{i}^2\end{bmatrix}$
$\Rightarrow\text{A}^2=\begin{bmatrix}-1&0\\0&-1\end{bmatrix}$ $(\because\ \text{i} ^2=-1)$

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 "2 Marks" from Algebra of Matrices→Algebra of Matrices — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If $\vec{\text{a}}=\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}},\ \vec{\text{b}}=4\hat{\text{i}}-2\hat{\text{j}}+3\hat{\text{k}}$and $\vec{\text{c}}=\hat{\text{i}}-2\hat{\text{j}}+\hat{\text{k}}$, find a vecctor of magnitude 6 units which is parallel to the vector $2\vec{\text{a}}-\vec{\text{b}}+3\vec{\text{c}}$.

Show that the direction cosines of a vector equally inclined to the axes OX, OY and OZ are $\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}}.$

Find the general solution of the differential equation $\left( {{e^x} + {\text{ }}{e^{ - x}}} \right){\text{ }}dy{\text{ }} - {\text{ }}\left( {{e^x} - {\text{ }}{e^{ - x}}} \right){\text{ }}dx{\text{ }} = {\text{ }}0$

Compute the products AB and BA whichever exists the following cases:
$\text{A}=\begin{bmatrix}1&-1&2&3\end{bmatrix}$ and $\text{B}=\begin{bmatrix}0\\1\\3\\2\end{bmatrix}$

In a group of 200 items, if the probability of getting a defective item is 0.2, write the mean of the distribution.

$\text{If y}=\begin{vmatrix}\text{f(x)} & \text{g(x)} & \text{h(x)} \\ \text{l} & \text{m} & \text{n} \\ \text{a} & \text{b} & \text{c} \end{vmatrix},\ \text{prove that}\frac{\text{dy}}{\text{dx}}= \begin{vmatrix}\text{f(x)} & \text{g'(x)} & \text{h'(x)} \\ \text{l} & \text{m} & \text{n} \\ \text{a} & \text{b} & \text{c}\end{vmatrix}$

Find which of the binary operations are commutative and which are associative.
State whether the following statements are true or false. Justify
If * is a commutative binary operation on N, then a * (b * c) = (c * b) * a

Evaluate the following integrals:
$\int\frac{\sin(\tan^{-1}\text{x})}{1+\text{x}^2}\text{ dx}$

Find the area of the parallelogram whose adjacent sides are determined by the vectors $\vec{a}=\hat{i}-\hat{j}+3 \hat{k}$ and $\vec{b}=2 \hat{i}-7 \hat{j}+\hat{k}$.

Reflexive and symmetric but not transitive.