$\"\"$

\

Multiply the matrix A(BC).

\

Substitute matrices B and C.

\

$\"\"$

\

Multiply columns by rows.

\

$\"\"$

\

$\"\"$ $\"\"$

\

Substitute matrix A

\

$\"\"$

\

Multiply columns by rows.

\

$\"\"$

\

$\"\"$ $\"\"$

\

Multiply the matrix (AB) C.

\

$\"\"$

\

Multiply columns by rows.

\

$\"\"$

\

$\"\"$ $\"\"$

\

Substitute matrix C.

\

$\"\"$

\

Multiply columns by rows.

\

$\"\"$

\

$\"\"$ $\"\"$

\

The solution of matrix A(BC) = (AB)C is True.