If A = [ * 20 c 0&1 0&0 ],I is the unit matrix of order 2 and a, … - Vidyadip

MCQ

If $A = \left[ {\begin{array}{*{20}{c}}0&1\\0&0\end{array}} \right],I$ is the unit matrix of order $2$ and $a, b$ are arbitrary constants, then ${(aI + bA)^2}$ is equal to

A
${a^2}I + abA$
✓
${a^2}I + 2abA$
C
${a^2}I + {b^2}A$
D
None of these

✓

Answer

Correct option: B.

${a^2}I + 2abA$

b
(b) ${(aI + bA)^2} = \left[ {\begin{array}{*{20}{c}}a&b\\0&a\end{array}} \right]\,\left[ {\begin{array}{*{20}{c}}a&b\\0&a\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}{{a^2}}&{2ab}\\0&{{a^2}}\end{array}} \right] = {a^2}I + 2abA$.

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