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  4. If A=[a b b2 -a2 -a b], then A2 is equal

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Q. If $A=\begin{bmatrix}a b & b^2 \\ -a^2 & -a b\end{bmatrix}$, then $A^2$ is equal

Matrices

Solution:

$A^2 =\begin{bmatrix} a b & b^2 \\ -a^2 & -a b \end{bmatrix}\begin{bmatrix} a b & b^2 \\ -a^2 & -a b \end{bmatrix}$
$ =\begin{bmatrix} a^2 b^2-a^2 b^2 & a b^3-a b^3 \\ -a^3 b+a^3 b & -a^2 b^2+a^2 b^2 \end{bmatrix}=O$