Answer
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Work Step by Step
Assume $\mathrm{C}$ be any nonzero $2 \times 3$ matrix. Define $A=\left[\begin{array}{cc}I_{3} & 0 \\ 0 & I_{3}\end{array}\right] .$ Then
$A^{2}=\left[\begin{array}{cc}I_{3} & 0 \\ C & -I_{2}\end{array}\right]\left[\begin{array}{cc}I_{3} & 0 \\ C & -I_{2}\end{array}\right]=\left[\begin{array}{cc}I_{3}+0 & 0+0 \\ C I_{3}-I_{2} C & 0+\left(-I_{2}\right)^{2}\end{array}\right]=\left[\begin{array}{cc}I_{3} & 0 \\ 0 & I_{3}\end{array}\right]$
