Equality of simple matrices

Here are three matrices:
$A=\left(\begin{array}{ll} 1 & 0 \\ 0 & 1 \\ 2 & 3 \end{array}\right), \quad B=\left(\begin{array}{ll} 1 & 0 \\ 0 & 1 \end{array}\right),\quad C=\left(\begin{array}{lll} 1 & 0 & 2 \\ 0 & 1 & 3 \end{array}\right)$ Are they distinct?

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Solution by Ancient Tree

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Yes, $A,B,C$ are three distinct matrices (meaning that $A\neq B$ , $A\neq C$ , and $B\neq C$ ), simply because their entries are different.
One might be tempted to say that $A$ and $C$ do have the same coefficients! But their dimensions are different, so they are not the same matrices.

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