78908 If \(A=\left[\begin{array}{ccc}1 & 2 & 2 \\ 2 & 1 & -2 \\ a & 2 & b\end{array}\right]\) is a matrix satisfying the equation \(A_{A} A^{2}=91\), where \(I\) is \(3 \times 3\) identity matrix, then the ordered pair \((a, b)\) is equal to

78909 Let \(\mathbf{A}\) be a \(3 \times 3\) matrix such that adj \(\mathbf{A}=\)
\(\left[\begin{array}{ccc} 2 & -1 & 1 \\ -1 & 0 & -2 \\ 1 & -2 & -1 \end{array}\right] \text { and } B=\operatorname{adj}(\operatorname{adj} A)\)
If \(|A| \lambda\) and \(\left|\left(B^{-1}\right)^{T}\right|=\mu\), then the ordered pair, \((|\lambda|, \mu)\) is equal to

78910 If \(A=\left(\begin{array}{cc}\frac{1}{\sqrt{5}} & \frac{2}{\sqrt{5}} \\ \frac{-2}{\sqrt{5}} & \frac{1}{\sqrt{5}}\end{array}\right), B=\left(\begin{array}{cc}1 & 0 \\ i & 1\end{array}\right), i=\sqrt{-1}\), and \(Q\) \(=A^{T} B A\), then the inverse of the matrix \(A Q^{2021}\) \(A^{\mathrm{T}}\) is equal to

78911 Let \(A=\left[\begin{array}{cc}1 & 2 \\ -1 & 4\end{array}\right]\). If \(A^{-1}=\alpha l+\beta A, \alpha, \beta \in R, l\) is a \(2 \times 2\) identity matrix, then \(4(\alpha-\beta)\) is equal to

78908 If \(A=\left[\begin{array}{ccc}1 & 2 & 2 \\ 2 & 1 & -2 \\ a & 2 & b\end{array}\right]\) is a matrix satisfying the equation \(A_{A} A^{2}=91\), where \(I\) is \(3 \times 3\) identity matrix, then the ordered pair \((a, b)\) is equal to

78909 Let \(\mathbf{A}\) be a \(3 \times 3\) matrix such that adj \(\mathbf{A}=\)
\(\left[\begin{array}{ccc} 2 & -1 & 1 \\ -1 & 0 & -2 \\ 1 & -2 & -1 \end{array}\right] \text { and } B=\operatorname{adj}(\operatorname{adj} A)\)
If \(|A| \lambda\) and \(\left|\left(B^{-1}\right)^{T}\right|=\mu\), then the ordered pair, \((|\lambda|, \mu)\) is equal to

78910 If \(A=\left(\begin{array}{cc}\frac{1}{\sqrt{5}} & \frac{2}{\sqrt{5}} \\ \frac{-2}{\sqrt{5}} & \frac{1}{\sqrt{5}}\end{array}\right), B=\left(\begin{array}{cc}1 & 0 \\ i & 1\end{array}\right), i=\sqrt{-1}\), and \(Q\) \(=A^{T} B A\), then the inverse of the matrix \(A Q^{2021}\) \(A^{\mathrm{T}}\) is equal to

78911 Let \(A=\left[\begin{array}{cc}1 & 2 \\ -1 & 4\end{array}\right]\). If \(A^{-1}=\alpha l+\beta A, \alpha, \beta \in R, l\) is a \(2 \times 2\) identity matrix, then \(4(\alpha-\beta)\) is equal to

78908 If \(A=\left[\begin{array}{ccc}1 & 2 & 2 \\ 2 & 1 & -2 \\ a & 2 & b\end{array}\right]\) is a matrix satisfying the equation \(A_{A} A^{2}=91\), where \(I\) is \(3 \times 3\) identity matrix, then the ordered pair \((a, b)\) is equal to

78909 Let \(\mathbf{A}\) be a \(3 \times 3\) matrix such that adj \(\mathbf{A}=\)
\(\left[\begin{array}{ccc} 2 & -1 & 1 \\ -1 & 0 & -2 \\ 1 & -2 & -1 \end{array}\right] \text { and } B=\operatorname{adj}(\operatorname{adj} A)\)
If \(|A| \lambda\) and \(\left|\left(B^{-1}\right)^{T}\right|=\mu\), then the ordered pair, \((|\lambda|, \mu)\) is equal to

78910 If \(A=\left(\begin{array}{cc}\frac{1}{\sqrt{5}} & \frac{2}{\sqrt{5}} \\ \frac{-2}{\sqrt{5}} & \frac{1}{\sqrt{5}}\end{array}\right), B=\left(\begin{array}{cc}1 & 0 \\ i & 1\end{array}\right), i=\sqrt{-1}\), and \(Q\) \(=A^{T} B A\), then the inverse of the matrix \(A Q^{2021}\) \(A^{\mathrm{T}}\) is equal to

78911 Let \(A=\left[\begin{array}{cc}1 & 2 \\ -1 & 4\end{array}\right]\). If \(A^{-1}=\alpha l+\beta A, \alpha, \beta \in R, l\) is a \(2 \times 2\) identity matrix, then \(4(\alpha-\beta)\) is equal to

78908 If \(A=\left[\begin{array}{ccc}1 & 2 & 2 \\ 2 & 1 & -2 \\ a & 2 & b\end{array}\right]\) is a matrix satisfying the equation \(A_{A} A^{2}=91\), where \(I\) is \(3 \times 3\) identity matrix, then the ordered pair \((a, b)\) is equal to

78909 Let \(\mathbf{A}\) be a \(3 \times 3\) matrix such that adj \(\mathbf{A}=\)
\(\left[\begin{array}{ccc} 2 & -1 & 1 \\ -1 & 0 & -2 \\ 1 & -2 & -1 \end{array}\right] \text { and } B=\operatorname{adj}(\operatorname{adj} A)\)
If \(|A| \lambda\) and \(\left|\left(B^{-1}\right)^{T}\right|=\mu\), then the ordered pair, \((|\lambda|, \mu)\) is equal to

78910 If \(A=\left(\begin{array}{cc}\frac{1}{\sqrt{5}} & \frac{2}{\sqrt{5}} \\ \frac{-2}{\sqrt{5}} & \frac{1}{\sqrt{5}}\end{array}\right), B=\left(\begin{array}{cc}1 & 0 \\ i & 1\end{array}\right), i=\sqrt{-1}\), and \(Q\) \(=A^{T} B A\), then the inverse of the matrix \(A Q^{2021}\) \(A^{\mathrm{T}}\) is equal to

78911 Let \(A=\left[\begin{array}{cc}1 & 2 \\ -1 & 4\end{array}\right]\). If \(A^{-1}=\alpha l+\beta A, \alpha, \beta \in R, l\) is a \(2 \times 2\) identity matrix, then \(4(\alpha-\beta)\) is equal to