Suppose that
Where a and b are real numbers. Show that
You must be able to mutilpy matrices in order to work these problems.
$\displaystyle
\left( {\begin{array}{*{20}c}
a & 0 \\
0 & b \\
\end{array} } \right) \cdot \left( {\begin{array}{*{20}c}
a & 0 \\
0 & b \\
\end{array} } \right) = \left( {\begin{array}{*{20}c}
{a \cdot a + 0 \cdot 0} & {a \cdot 0 + 0 \cdot b} \\
{0 \cdot a + b \cdot 0} & {0 \cdot 0 + b \cdot b} \\
\end{array} } \right) = \left( {\begin{array}{*{20}c}
{a^2 } & 0 \\
0 & {b^2 } \\
\end{array} } \right)$
Yes, one would do this problem using induction. You are correct about that.
However, that is not the point. In order to do this problem you must learn to do matrix multiplication.
Without knowing how to do that, there is no hope of doing this problem.
So you must learn matrix multiplication. (Note we don’t teach here).