First slide

Operations of matrix

Question

If $A = [\begin{array}{cc} 0 & - i \\ i & 0 \end{array}], B = [\begin{array}{cc} 1 & 0 \\ 0 & - 1 \end{array}]$ ,then $A B + B A$ is

Easy

A

null matrix
B

unit matrix
C

invertible matrix
D

none of these

Solution

$A B = [\begin{array}{cc} 0 & - i \\ i & 0 \end{array}] [\begin{array}{cc} 1 & 0 \\ 0 & - 1 \end{array}] = [\begin{array}{ll} 0 i \\ i 0 \end{array}]$
and $B A = [\begin{array}{cc} 1 & 0 \\ 0 & - 1 \end{array}] [\begin{array}{cc} 0 & - i \\ i & 0 \end{array}] = [\begin{array}{cc} 0 & - i \\ - i & 0 \end{array}]$
Thus, $A B + B A = O$

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