Answers: 3
is given as![B = A + 2I = \left[\begin{array}{cc}4&0\\0&4\end{array}\right]](/tpl/images/0074/0331/96516.png)
![A = \left[\begin{array}{cc}2&0\\0&2\end{array}\right]](/tpl/images/0074/0331/8c9df.png)
)
to imply 
be its left inverse, then 
(
is identity matrix)![AB = A^2 + 2A\\A(B) = A(A + 2I_2)\\\\\Multiplying L_{A}\text{ on left side of both terms,}\\\\L_{A} AB = L_{A}A(A + 2I_2)\\B = A + 2I_2\\\\B = \left[\begin{array}{cc}2&0\\0&2\end{array}\right] + \left[\begin{array}{cc}2&0\\0&2\end{array}\right] = \left[\begin{array}{cc}4&0\\0&4\end{array}\right] = 4I_2\\\\B = 4I_2](/tpl/images/0074/0331/68877.png)
![B = \left[\begin{array}{cc}4&0\\0&4\end{array}\right]](/tpl/images/0074/0331/d1ee0.png)
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If possible, find a matrix b such that ab = a2 + 2a....
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