IfA= ((-1,0),(0,2))  then(A³-A²)=? 

Explanation:

Another Explanation (5): দেওয়া আছে, \( A = \begin{pmatrix} -1 & 0 \\ 0 & 2 \end{pmatrix} \) \( A^2 = A \cdot A = \begin{pmatrix} -1 & 0 \\ 0 & 2 \end{pmatrix} \begin{pmatrix} -1 & 0 \\ 0 & 2 \end{pmatrix} = \begin{pmatrix} 1 & 0 \\ 0 & 4 \end{pmatrix} \) \( A^3 = A^2 \cdot A = \begin{pmatrix} 1 & 0 \\ 0 & 4 \end{pmatrix} \begin{pmatrix} -1 & 0 \\ 0 & 2 \end{pmatrix} = \begin{pmatrix} -1 & 0 \\ 0 & 8 \end{pmatrix} \) এখন, \( A^3 - A^2 = \begin{pmatrix} -1 & 0 \\ 0 & 8 \end{pmatrix} - \begin{pmatrix} 1 & 0 \\ 0 & 4 \end{pmatrix} = \begin{pmatrix} -2 & 0 \\ 0 & 4 \end{pmatrix} \) আবার, \( 2A = 2 \begin{pmatrix} -1 & 0 \\ 0 & 2 \end{pmatrix} = \begin{pmatrix} -2 & 0 \\ 0 & 4 \end{pmatrix} \) সুতরাং, \( A^3 - A^2 = 2A \) 🥳