Question

If Pythagorean triple $(a,b,c)$ is written as row matrix $\left[abc\right]$ then which of the following matrix a product is not a Pythagorean triplet?

• A. $\left[345\right]A$
• B. $\left[345\right]B$
• C. $\left[345\right]C$
• D. None of these

Answer 1

The correct option is A $\left[345\right]A$

Option A

$\left[\begin{array}{ccc}3& 4& 5\end{array}\right]A$

$=\left[\begin{array}{ccc}3& 4& 5\end{array}\right]\left[\begin{array}{ccc}1& 2& 3\\ 2& 1& 1\\ 2& 2& 3\end{array}\right]$

$=\left[\begin{array}{ccc}3+8+10& 6+4+10& 9+4+15\end{array}\right]$

$=\left[\begin{array}{ccc}21& 20& 20\end{array}\right]$

Not a triplet

Option B

$\left[\begin{array}{ccc}3& 4& 5\end{array}\right]\left[\begin{array}{ccc}1& 2& 2\\ -2& -1& -2\\ 2& 2& 3\end{array}\right]$

$=\left[\begin{array}{ccc}5& 12& 13\end{array}\right]$ Yes a triplet

Option C:

$\left[\begin{array}{ccc}3& 4& 5\end{array}\right]\left[\begin{array}{ccc}-1& -2& -2\\ 2& 1& 2\\ 2& 2& 3\end{array}\right]$

$=\left[\begin{array}{ccc}15& 8& 17\end{array}\right]$-Yes a triplet

Option A