Question

[tex] If A=\left[\begin{array}{ccc}ab&b²\\a²&-ab\end{array}\right], then obtain A². [\tex]

Answer 1

Answer:

$\left[\begin{array}{ccc}2a^{2}b^{2}&0\\0&2a^{2}b^{2}\end{array}\right]$

Step-by-step explanation:

$A=\left[\begin{array}{ccc}ab&b^{2} \\a^{2} &-ab\end{array}\right]\\A^{2} =\left[\begin{array}{ccc}ab&b^{2} \\a^{2} &-ab\end{array}\right]\times \left[\begin{array}{ccc}ab&b^2\\a^2&-ab\end{array}\right]\\=\left[\begin{array}{ccc}a^{2}b^{2}+a^{2}b^{2} &0\\0&a^{2}b^{2}+a^{2}b^{2}\end{array}\right]\\=\left[\begin{array}{ccc}2a^{2}b^{2}&0\\0&2a^{2}b^{2}\end{array}\right]$