$\"\"$

\

Multiply the matrix X(YZ).

\

Substitute matrices Y and Z.

\

$\"\"$

\

Multiply columns by rows.

\

$\"\"$

\

$\"\"$ (Simplify) $\"\"$

\

Substitute matrix X

\

$\"\"$

\

Multiply columns by rows.

\

$\"\"$

\

$\"\"$ (Simplify)

\

\

$\"\"$ (Simplify) $\"\"$

\

Multiply the matrix (XY)Z.

\

$\"\"$

\

Multiply columns by rows.

\

$\"\"$

\

$\"\"$ (Simplify)

\

$\"\"$ (Simplify)

\

$\"\"$

\

Substitute matrix Z

\

$\"\"$

\

Multiply columns by rows.

\

$\"\"$

\

$\"\"$ (Simplify)

\

$\"\"$ (Simplify) $\"\"$

\

The solution of matrix X(YZ) = (XY)Z is True.