If A = dig(2, - 1, ,3),B = dig( - 1, ,3, ,2), then A^2 B = - Vidyadip

MCQ

If $A = dig(2, - 1,\,3),B = dig( - 1,\,3,\,2)$, then ${A^2}B = $

A
$dig\ (5, 4, 11)$
✓
$dig\ (-4, 3, 18)$
C
$dig\ (3, 1, 8 )$
D
$B$

✓

Answer

Correct option: B.

$dig\ (-4, 3, 18)$

b
(b) ${A^2}B = (A.\,A)B = \left[ {\begin{array}{*{20}{c}}2&0&0\\0&{ - 1}&0\\0&0&3\end{array}} \right]\,\left[ {\begin{array}{*{20}{c}}2&0&0\\0&{ - 1}&0\\0&0&3\end{array}} \right].\,\left[ {\begin{array}{*{20}{c}}{ - 1}&0&0\\0&3&0\\0&0&2\end{array}} \right]$

$ = \left[ {\begin{array}{*{20}{c}}4&0&0\\0&1&0\\0&0&9\end{array}} \right]\,\left[ {\begin{array}{*{20}{c}}{ - 1}&0&0\\0&3&0\\0&0&2\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}{ - 4}&0&0\\0&3&0\\0&0&{18}\end{array}} \right]$.

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