78848 Let \(A\) be a \(2 \times 2\) matrix with \(\operatorname{det}(A)=-1\) and \(\operatorname{det}((A+I) \operatorname{adj}(A)+I))=4\). Then the sum of the diagonal elements of \(A\) can be :

78849 Let \(A\) be a matrix of order \(3 \times 3\) and det \((A)=\) 2. Then \(\operatorname{det}\left(\operatorname{det}(\mathrm{A}) \operatorname{adj}\left(5 \operatorname{adj}\left(\mathrm{A}^{3}\right)\right)\right)\) is equal to

78850 Let \(x, y, z>1\) and \(A=\left[\begin{array}{ccc}\log _{y} x & 2 & \log _{y} z \\ \log _{z} x & \log _{z} y & 3\end{array}\right]\).
The \(\left|\operatorname{adj}\left(\operatorname{adj} \mathbf{A}_{8}^{2}\right)\right|\) is equal to

78851 Let \(A=\left[\begin{array}{cc}\frac{1}{\sqrt{10}} & \frac{3}{\sqrt{10}} \\ \frac{-3}{\sqrt{10}} & \frac{1}{\sqrt{10}}\end{array}\right]\) and \(B=\left[\begin{array}{cc}1 & -i \\ 0 & 1\end{array}\right]\), where \(\mathbf{i}=\sqrt{-1}\) If \(M=A^{\mathrm{T}} \mathbf{B} A\), then the inverse of the matrix \(A M^{2023} A^{T}\) is

78852 If \(P\) is a \(3 \times 3\) real matrix such that \(P^{\mathrm{T}}=\mathbf{a P}+(\mathrm{a}\) -1) I, Where a \(>1\), then

78848 Let \(A\) be a \(2 \times 2\) matrix with \(\operatorname{det}(A)=-1\) and \(\operatorname{det}((A+I) \operatorname{adj}(A)+I))=4\). Then the sum of the diagonal elements of \(A\) can be :

78849 Let \(A\) be a matrix of order \(3 \times 3\) and det \((A)=\) 2. Then \(\operatorname{det}\left(\operatorname{det}(\mathrm{A}) \operatorname{adj}\left(5 \operatorname{adj}\left(\mathrm{A}^{3}\right)\right)\right)\) is equal to

78850 Let \(x, y, z>1\) and \(A=\left[\begin{array}{ccc}\log _{y} x & 2 & \log _{y} z \\ \log _{z} x & \log _{z} y & 3\end{array}\right]\).
The \(\left|\operatorname{adj}\left(\operatorname{adj} \mathbf{A}_{8}^{2}\right)\right|\) is equal to

78851 Let \(A=\left[\begin{array}{cc}\frac{1}{\sqrt{10}} & \frac{3}{\sqrt{10}} \\ \frac{-3}{\sqrt{10}} & \frac{1}{\sqrt{10}}\end{array}\right]\) and \(B=\left[\begin{array}{cc}1 & -i \\ 0 & 1\end{array}\right]\), where \(\mathbf{i}=\sqrt{-1}\) If \(M=A^{\mathrm{T}} \mathbf{B} A\), then the inverse of the matrix \(A M^{2023} A^{T}\) is

78852 If \(P\) is a \(3 \times 3\) real matrix such that \(P^{\mathrm{T}}=\mathbf{a P}+(\mathrm{a}\) -1) I, Where a \(>1\), then

78848 Let \(A\) be a \(2 \times 2\) matrix with \(\operatorname{det}(A)=-1\) and \(\operatorname{det}((A+I) \operatorname{adj}(A)+I))=4\). Then the sum of the diagonal elements of \(A\) can be :

78849 Let \(A\) be a matrix of order \(3 \times 3\) and det \((A)=\) 2. Then \(\operatorname{det}\left(\operatorname{det}(\mathrm{A}) \operatorname{adj}\left(5 \operatorname{adj}\left(\mathrm{A}^{3}\right)\right)\right)\) is equal to

78850 Let \(x, y, z>1\) and \(A=\left[\begin{array}{ccc}\log _{y} x & 2 & \log _{y} z \\ \log _{z} x & \log _{z} y & 3\end{array}\right]\).
The \(\left|\operatorname{adj}\left(\operatorname{adj} \mathbf{A}_{8}^{2}\right)\right|\) is equal to

78851 Let \(A=\left[\begin{array}{cc}\frac{1}{\sqrt{10}} & \frac{3}{\sqrt{10}} \\ \frac{-3}{\sqrt{10}} & \frac{1}{\sqrt{10}}\end{array}\right]\) and \(B=\left[\begin{array}{cc}1 & -i \\ 0 & 1\end{array}\right]\), where \(\mathbf{i}=\sqrt{-1}\) If \(M=A^{\mathrm{T}} \mathbf{B} A\), then the inverse of the matrix \(A M^{2023} A^{T}\) is

78852 If \(P\) is a \(3 \times 3\) real matrix such that \(P^{\mathrm{T}}=\mathbf{a P}+(\mathrm{a}\) -1) I, Where a \(>1\), then

78848 Let \(A\) be a \(2 \times 2\) matrix with \(\operatorname{det}(A)=-1\) and \(\operatorname{det}((A+I) \operatorname{adj}(A)+I))=4\). Then the sum of the diagonal elements of \(A\) can be :

78849 Let \(A\) be a matrix of order \(3 \times 3\) and det \((A)=\) 2. Then \(\operatorname{det}\left(\operatorname{det}(\mathrm{A}) \operatorname{adj}\left(5 \operatorname{adj}\left(\mathrm{A}^{3}\right)\right)\right)\) is equal to

78850 Let \(x, y, z>1\) and \(A=\left[\begin{array}{ccc}\log _{y} x & 2 & \log _{y} z \\ \log _{z} x & \log _{z} y & 3\end{array}\right]\).
The \(\left|\operatorname{adj}\left(\operatorname{adj} \mathbf{A}_{8}^{2}\right)\right|\) is equal to

78851 Let \(A=\left[\begin{array}{cc}\frac{1}{\sqrt{10}} & \frac{3}{\sqrt{10}} \\ \frac{-3}{\sqrt{10}} & \frac{1}{\sqrt{10}}\end{array}\right]\) and \(B=\left[\begin{array}{cc}1 & -i \\ 0 & 1\end{array}\right]\), where \(\mathbf{i}=\sqrt{-1}\) If \(M=A^{\mathrm{T}} \mathbf{B} A\), then the inverse of the matrix \(A M^{2023} A^{T}\) is

78852 If \(P\) is a \(3 \times 3\) real matrix such that \(P^{\mathrm{T}}=\mathbf{a P}+(\mathrm{a}\) -1) I, Where a \(>1\), then

78848 Let \(A\) be a \(2 \times 2\) matrix with \(\operatorname{det}(A)=-1\) and \(\operatorname{det}((A+I) \operatorname{adj}(A)+I))=4\). Then the sum of the diagonal elements of \(A\) can be :

78849 Let \(A\) be a matrix of order \(3 \times 3\) and det \((A)=\) 2. Then \(\operatorname{det}\left(\operatorname{det}(\mathrm{A}) \operatorname{adj}\left(5 \operatorname{adj}\left(\mathrm{A}^{3}\right)\right)\right)\) is equal to

78850 Let \(x, y, z>1\) and \(A=\left[\begin{array}{ccc}\log _{y} x & 2 & \log _{y} z \\ \log _{z} x & \log _{z} y & 3\end{array}\right]\).
The \(\left|\operatorname{adj}\left(\operatorname{adj} \mathbf{A}_{8}^{2}\right)\right|\) is equal to

78851 Let \(A=\left[\begin{array}{cc}\frac{1}{\sqrt{10}} & \frac{3}{\sqrt{10}} \\ \frac{-3}{\sqrt{10}} & \frac{1}{\sqrt{10}}\end{array}\right]\) and \(B=\left[\begin{array}{cc}1 & -i \\ 0 & 1\end{array}\right]\), where \(\mathbf{i}=\sqrt{-1}\) If \(M=A^{\mathrm{T}} \mathbf{B} A\), then the inverse of the matrix \(A M^{2023} A^{T}\) is

78852 If \(P\) is a \(3 \times 3\) real matrix such that \(P^{\mathrm{T}}=\mathbf{a P}+(\mathrm{a}\) -1) I, Where a \(>1\), then