First slide

Operations of matrix

Question

If $A = [\begin{array}{ll} i 0 \\ 0 i \end{array}], n \in N,$ then $A^{4 n}$ equals

Moderate

A

$[\begin{array}{ll} 0 i \\ i 0 \end{array}]$
B

$[\begin{array}{ll} 0 0 \\ i 0 \end{array}]$
C

$[\begin{array}{ll} 1 0 \\ 0 1 \end{array}]$
D

$[\begin{array}{ll} 0 - i \\ i 0 \end{array}]$

Solution

We have, $A = [\begin{array}{ll} i 0 \\ 0 i \end{array}]$
Clearly, A is a diagonal matrix. Therefore, $A^{4 n}$ is also a diagonal matrix such that
$A^{4 n} = [\begin{array}{cc} i^{4 n} & 0 \\ 0 & i^{4 n} \end{array}] = [\begin{array}{ll} 1 0 \\ 0 1 \end{array}]$

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