First slide

Applications of determinant

Question

If $A = \frac{1}{2} (\begin{array}{cc} 1 & \sqrt{3} \\ \sqrt{3} & - 1 \end{array}),$ then $A^{- 1} - A^{2}$

Moderate

A

null matrix
B

invertible matrix
C

unit matrix
D

none of these

Solution

$A = (\begin{array}{cc} - 1 / 2 & - \sqrt{3} / 2 \\ \sqrt{3} / 2 & - 1 / 2 \end{array}) = (\begin{array}{cc} \cos (4 π / 3) & \sin (4 π / 3) \\ - \sin (4 π / 3) & \cos (4 π / 3) \end{array})$
Note that $A^{3} = I \Rightarrow A^{2} - A^{- 1} = O$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App