(%i1) A : matrix ( [ 2 , 3 ] , [ − 8 , 1 ] ) ;

\[\operatorname{ }\begin{pmatrix}2 & 3\\ -8 & 1\end{pmatrix}\]

(%i2) B : matrix ( [ − 2 , 7 ] , [ 1 , 2 ] ) ;

\[\operatorname{ }\begin{pmatrix}-2 & 7\\ 1 & 2\end{pmatrix}\]

(%i3) I : ident ( 2 ) ;

\[\operatorname{ }\begin{pmatrix}1 & 0\\ 0 & 1\end{pmatrix}\]

1 a) dio

(%i4) A ^ ^ 2 ;

\[\operatorname{ }\begin{pmatrix}-20 & 9\\ -24 & -23\end{pmatrix}\]

(%i5) I − A ^ ^ 2 ;

\[\operatorname{ }\begin{pmatrix}21 & -9\\ 24 & 24\end{pmatrix}\]

(%i6) I − A ;

\[\operatorname{ }\begin{pmatrix}-1 & -3\\ 8 & 0\end{pmatrix}\]

(%i7) I + A ;

\[\operatorname{ }\begin{pmatrix}3 & 3\\ -8 & 2\end{pmatrix}\]

(%i8) ( I − A ) . ( I + A ) ;

\[\operatorname{ }\begin{pmatrix}21 & -9\\ 24 & 24\end{pmatrix}\]

(%i9) ( I + A ) . ( I − A ) ;

\[\operatorname{ }\begin{pmatrix}21 & -9\\ 24 & 24\end{pmatrix}\]

2 b) dio

(%i10) A ^ ^ 2 ;

\[\operatorname{ }\begin{pmatrix}-20 & 9\\ -24 & -23\end{pmatrix}\]

(%i11) B ^ ^ 2 ;

\[\operatorname{ }\begin{pmatrix}11 & 0\\ 0 & 11\end{pmatrix}\]

(%i12) A ^ ^ 2 − B ^ ^ 2 ;

\[\operatorname{ }\begin{pmatrix}-31 & 9\\ -24 & -34\end{pmatrix}\]

(%i13) A − B ;

\[\operatorname{ }\begin{pmatrix}4 & -4\\ -9 & -1\end{pmatrix}\]

(%i14) A + B ;

\[\operatorname{ }\begin{pmatrix}0 & 10\\ -7 & 3\end{pmatrix}\]

(%i15) ( A − B ) . ( A + B ) ;

\[\operatorname{ }\begin{pmatrix}28 & 28\\ 7 & -93\end{pmatrix}\]

(%i16) ( A + B ) . ( A − B ) ;

\[\operatorname{ }\begin{pmatrix}-90 & -10\\ -55 & 25\end{pmatrix}\]

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