Matrix Multiplication

Solution:

Multiply row by column:

\[ = \begin{bmatrix} a\cdot a + b\cdot b & a(-b) + b\cdot a \\ -b\cdot a + a\cdot b & (-b)(-b) + a\cdot a \end{bmatrix} \] \[ = \begin{bmatrix} a^2 + b^2 & -ab + ab \\ -ab + ab & b^2 + a^2 \end{bmatrix} \] \[ = \begin{bmatrix} a^2 + b^2 & 0 \\ 0 & a^2 + b^2 \end{bmatrix} \]

Final Answer:

\[ \boxed{ (a^2 + b^2) \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} } \]

This shows the product is a scalar multiple of the identity matrix.