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

MCQ

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

✓
Unit matrix
B
Null matrix
C
$A$
D
$-A$

✓

Answer

Correct option: A.

Unit matrix

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

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