78886
If \(A\) and \(B\) square matrices of the same order and \(A B=3 I\), then \(A^{-1}\) is equal to
1 \(3 \mathrm{~B}\)
2 \(\frac{1}{3} \mathrm{~B}\)
3 \(3 \mathrm{~B}^{-1}\)
4 \(\frac{1}{3} \mathrm{~B}^{-1}\)
Explanation:
(B) : Given, \(A\) and \(B\) are square matrices of same order and \(\mathrm{AB}=3 \mathrm{I}\) \(\mathrm{A}^{-1} \mathrm{AB}=3 \mathrm{IA}^{-1}\) \(\mathrm{~B}=3 \mathrm{~A}^{-1}\) \(\mathrm{~A}^{-1}=\frac{\mathrm{B}}{3}\)
WB JEE-2009
Matrix and Determinant
78887
If the inverse of the matrix \(A=\left[\begin{array}{ccc}3 & 4 & 5 \\ 2 & -1 & 8 \\ 5 & -2 & 7\end{array}\right]\) is \(B\), then \(\mathbf{B}^{\mathrm{T}}=\)
78886
If \(A\) and \(B\) square matrices of the same order and \(A B=3 I\), then \(A^{-1}\) is equal to
1 \(3 \mathrm{~B}\)
2 \(\frac{1}{3} \mathrm{~B}\)
3 \(3 \mathrm{~B}^{-1}\)
4 \(\frac{1}{3} \mathrm{~B}^{-1}\)
Explanation:
(B) : Given, \(A\) and \(B\) are square matrices of same order and \(\mathrm{AB}=3 \mathrm{I}\) \(\mathrm{A}^{-1} \mathrm{AB}=3 \mathrm{IA}^{-1}\) \(\mathrm{~B}=3 \mathrm{~A}^{-1}\) \(\mathrm{~A}^{-1}=\frac{\mathrm{B}}{3}\)
WB JEE-2009
Matrix and Determinant
78887
If the inverse of the matrix \(A=\left[\begin{array}{ccc}3 & 4 & 5 \\ 2 & -1 & 8 \\ 5 & -2 & 7\end{array}\right]\) is \(B\), then \(\mathbf{B}^{\mathrm{T}}=\)
78886
If \(A\) and \(B\) square matrices of the same order and \(A B=3 I\), then \(A^{-1}\) is equal to
1 \(3 \mathrm{~B}\)
2 \(\frac{1}{3} \mathrm{~B}\)
3 \(3 \mathrm{~B}^{-1}\)
4 \(\frac{1}{3} \mathrm{~B}^{-1}\)
Explanation:
(B) : Given, \(A\) and \(B\) are square matrices of same order and \(\mathrm{AB}=3 \mathrm{I}\) \(\mathrm{A}^{-1} \mathrm{AB}=3 \mathrm{IA}^{-1}\) \(\mathrm{~B}=3 \mathrm{~A}^{-1}\) \(\mathrm{~A}^{-1}=\frac{\mathrm{B}}{3}\)
WB JEE-2009
Matrix and Determinant
78887
If the inverse of the matrix \(A=\left[\begin{array}{ccc}3 & 4 & 5 \\ 2 & -1 & 8 \\ 5 & -2 & 7\end{array}\right]\) is \(B\), then \(\mathbf{B}^{\mathrm{T}}=\)
78886
If \(A\) and \(B\) square matrices of the same order and \(A B=3 I\), then \(A^{-1}\) is equal to
1 \(3 \mathrm{~B}\)
2 \(\frac{1}{3} \mathrm{~B}\)
3 \(3 \mathrm{~B}^{-1}\)
4 \(\frac{1}{3} \mathrm{~B}^{-1}\)
Explanation:
(B) : Given, \(A\) and \(B\) are square matrices of same order and \(\mathrm{AB}=3 \mathrm{I}\) \(\mathrm{A}^{-1} \mathrm{AB}=3 \mathrm{IA}^{-1}\) \(\mathrm{~B}=3 \mathrm{~A}^{-1}\) \(\mathrm{~A}^{-1}=\frac{\mathrm{B}}{3}\)
WB JEE-2009
Matrix and Determinant
78887
If the inverse of the matrix \(A=\left[\begin{array}{ccc}3 & 4 & 5 \\ 2 & -1 & 8 \\ 5 & -2 & 7\end{array}\right]\) is \(B\), then \(\mathbf{B}^{\mathrm{T}}=\)
