78892 If \(A=\left[\begin{array}{ccc}1 & 2 & 3 \\ 1 & 1 & 1 \\ 1 & -1 & 1\end{array}\right], B=\left[\begin{array}{lll}1 & 1 & 0 \\ 0 & 1 & 3 \\ 3 & 0 & 4\end{array}\right]\)
\(\mathbf{C}=\left[\begin{array}{lll}2 & 0 & 1 \\ 0 & 1 & 0 \\ 3 & 2 & 1\end{array}\right], \operatorname{then}\left(\left(\left((A B C)^{-1}\right)^{\mathrm{T}}\right)^{-1}\right)^{\mathrm{T}}=\)

78893 Let \(A, B, C, D\) be square real matrices such that \(\mathbf{C}^{\mathrm{T}}=\mathrm{DAB}, \mathrm{D}^{\mathrm{T}}=\mathrm{ABC}, \mathrm{S}=\mathrm{ABCD}\) then \(\mathrm{S}^{2}\) is equal to

78895 The value of \(\left|\begin{array}{ccc}x+y & y+z & z+x \\ x & y & z \\ x-y & y-z & z-x\end{array}\right|\) is equal to :

78896 Let \(A=\left[\begin{array}{ccc}1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1\end{array}\right]\) and \(10 B=\left[\begin{array}{ccc}4 & 2 & 2 \\ -5 & 0 & \alpha \\ 1 & -2 & 3\end{array}\right]\).If
\(B\) is the inverse of matrix \(A\), then \(\alpha\) is

78899 Let \(A=\left(\begin{array}{ll}1 & 2 \\ 2 & 1\end{array}\right) . \quad\) The determinant of \(\frac{1}{3} \mathrm{~A}(\operatorname{adj}(\operatorname{adj} \mathrm{A}))\) is

78892 If \(A=\left[\begin{array}{ccc}1 & 2 & 3 \\ 1 & 1 & 1 \\ 1 & -1 & 1\end{array}\right], B=\left[\begin{array}{lll}1 & 1 & 0 \\ 0 & 1 & 3 \\ 3 & 0 & 4\end{array}\right]\)
\(\mathbf{C}=\left[\begin{array}{lll}2 & 0 & 1 \\ 0 & 1 & 0 \\ 3 & 2 & 1\end{array}\right], \operatorname{then}\left(\left(\left((A B C)^{-1}\right)^{\mathrm{T}}\right)^{-1}\right)^{\mathrm{T}}=\)

78893 Let \(A, B, C, D\) be square real matrices such that \(\mathbf{C}^{\mathrm{T}}=\mathrm{DAB}, \mathrm{D}^{\mathrm{T}}=\mathrm{ABC}, \mathrm{S}=\mathrm{ABCD}\) then \(\mathrm{S}^{2}\) is equal to

78895 The value of \(\left|\begin{array}{ccc}x+y & y+z & z+x \\ x & y & z \\ x-y & y-z & z-x\end{array}\right|\) is equal to :

78896 Let \(A=\left[\begin{array}{ccc}1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1\end{array}\right]\) and \(10 B=\left[\begin{array}{ccc}4 & 2 & 2 \\ -5 & 0 & \alpha \\ 1 & -2 & 3\end{array}\right]\).If
\(B\) is the inverse of matrix \(A\), then \(\alpha\) is

78899 Let \(A=\left(\begin{array}{ll}1 & 2 \\ 2 & 1\end{array}\right) . \quad\) The determinant of \(\frac{1}{3} \mathrm{~A}(\operatorname{adj}(\operatorname{adj} \mathrm{A}))\) is

78892 If \(A=\left[\begin{array}{ccc}1 & 2 & 3 \\ 1 & 1 & 1 \\ 1 & -1 & 1\end{array}\right], B=\left[\begin{array}{lll}1 & 1 & 0 \\ 0 & 1 & 3 \\ 3 & 0 & 4\end{array}\right]\)
\(\mathbf{C}=\left[\begin{array}{lll}2 & 0 & 1 \\ 0 & 1 & 0 \\ 3 & 2 & 1\end{array}\right], \operatorname{then}\left(\left(\left((A B C)^{-1}\right)^{\mathrm{T}}\right)^{-1}\right)^{\mathrm{T}}=\)

78893 Let \(A, B, C, D\) be square real matrices such that \(\mathbf{C}^{\mathrm{T}}=\mathrm{DAB}, \mathrm{D}^{\mathrm{T}}=\mathrm{ABC}, \mathrm{S}=\mathrm{ABCD}\) then \(\mathrm{S}^{2}\) is equal to

78895 The value of \(\left|\begin{array}{ccc}x+y & y+z & z+x \\ x & y & z \\ x-y & y-z & z-x\end{array}\right|\) is equal to :

78896 Let \(A=\left[\begin{array}{ccc}1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1\end{array}\right]\) and \(10 B=\left[\begin{array}{ccc}4 & 2 & 2 \\ -5 & 0 & \alpha \\ 1 & -2 & 3\end{array}\right]\).If
\(B\) is the inverse of matrix \(A\), then \(\alpha\) is

78899 Let \(A=\left(\begin{array}{ll}1 & 2 \\ 2 & 1\end{array}\right) . \quad\) The determinant of \(\frac{1}{3} \mathrm{~A}(\operatorname{adj}(\operatorname{adj} \mathrm{A}))\) is

78892 If \(A=\left[\begin{array}{ccc}1 & 2 & 3 \\ 1 & 1 & 1 \\ 1 & -1 & 1\end{array}\right], B=\left[\begin{array}{lll}1 & 1 & 0 \\ 0 & 1 & 3 \\ 3 & 0 & 4\end{array}\right]\)
\(\mathbf{C}=\left[\begin{array}{lll}2 & 0 & 1 \\ 0 & 1 & 0 \\ 3 & 2 & 1\end{array}\right], \operatorname{then}\left(\left(\left((A B C)^{-1}\right)^{\mathrm{T}}\right)^{-1}\right)^{\mathrm{T}}=\)

78893 Let \(A, B, C, D\) be square real matrices such that \(\mathbf{C}^{\mathrm{T}}=\mathrm{DAB}, \mathrm{D}^{\mathrm{T}}=\mathrm{ABC}, \mathrm{S}=\mathrm{ABCD}\) then \(\mathrm{S}^{2}\) is equal to

78895 The value of \(\left|\begin{array}{ccc}x+y & y+z & z+x \\ x & y & z \\ x-y & y-z & z-x\end{array}\right|\) is equal to :

78896 Let \(A=\left[\begin{array}{ccc}1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1\end{array}\right]\) and \(10 B=\left[\begin{array}{ccc}4 & 2 & 2 \\ -5 & 0 & \alpha \\ 1 & -2 & 3\end{array}\right]\).If
\(B\) is the inverse of matrix \(A\), then \(\alpha\) is

78899 Let \(A=\left(\begin{array}{ll}1 & 2 \\ 2 & 1\end{array}\right) . \quad\) The determinant of \(\frac{1}{3} \mathrm{~A}(\operatorname{adj}(\operatorname{adj} \mathrm{A}))\) is

78892 If \(A=\left[\begin{array}{ccc}1 & 2 & 3 \\ 1 & 1 & 1 \\ 1 & -1 & 1\end{array}\right], B=\left[\begin{array}{lll}1 & 1 & 0 \\ 0 & 1 & 3 \\ 3 & 0 & 4\end{array}\right]\)
\(\mathbf{C}=\left[\begin{array}{lll}2 & 0 & 1 \\ 0 & 1 & 0 \\ 3 & 2 & 1\end{array}\right], \operatorname{then}\left(\left(\left((A B C)^{-1}\right)^{\mathrm{T}}\right)^{-1}\right)^{\mathrm{T}}=\)

78893 Let \(A, B, C, D\) be square real matrices such that \(\mathbf{C}^{\mathrm{T}}=\mathrm{DAB}, \mathrm{D}^{\mathrm{T}}=\mathrm{ABC}, \mathrm{S}=\mathrm{ABCD}\) then \(\mathrm{S}^{2}\) is equal to

78895 The value of \(\left|\begin{array}{ccc}x+y & y+z & z+x \\ x & y & z \\ x-y & y-z & z-x\end{array}\right|\) is equal to :

78896 Let \(A=\left[\begin{array}{ccc}1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1\end{array}\right]\) and \(10 B=\left[\begin{array}{ccc}4 & 2 & 2 \\ -5 & 0 & \alpha \\ 1 & -2 & 3\end{array}\right]\).If
\(B\) is the inverse of matrix \(A\), then \(\alpha\) is

78899 Let \(A=\left(\begin{array}{ll}1 & 2 \\ 2 & 1\end{array}\right) . \quad\) The determinant of \(\frac{1}{3} \mathrm{~A}(\operatorname{adj}(\operatorname{adj} \mathrm{A}))\) is