If A = [ * 20 c - 1 &0&0 0& - 1 &0 0&0& - 1 ], then A^2 is

MCQ

If $A = \left[ {\begin{array}{*{20}{c}}{ - 1}&0&0\\0&{ - 1}&0\\0&0&{ - 1}\end{array}} \right]$, then ${A^2}$is

A
Null matrix
✓
Unit matrix
C
$A$
D
$2A$

✓

Answer

Correct option: B.

Unit matrix

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

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