Matrices And Determinants - Algebra - Mathematics Previous Year Questions

If \(A^{-1}=\left[\begin{array}{rr}5 & -2 \\ -7 & 3\end{array}\right]\) and \(B^{-1}=\frac{1}{2}\left[\begin{array}{rr}9 & -7 \\ -8 & 6\end{array}\right]\), then \((A B)^{-1}\) is equal to

If \(A=\left[\begin{array}{ll}3 & -4 \\ 1 & -1\end{array}\right]\), then \(\left(A-A^{\prime}\right)\) is equal to (where, \(A^{\prime}\) is transpose of matrix \(A\) )

For all values of \(\lambda\), rank of matrix

$$A=\left[\begin{array}{ccc} { }^h C_0 & { }^4 C_3 & { }^5 C_4 \\ \[\lambda & 8 & 8 \lambda-6 \\\] 1+\lambda^2 & 8 \lambda+4 & 2 \lambda+21 \end{array}\right]$$

If matrix \(A=\left[\begin{array}{ccc}0 & 2 b & -2 \\ 3 & 1 & 3 \\ 3 a & 3 & -1\end{array}\right]\) is given to be symmetric, then the value of \(a b\) is

Suppose, \(A=\left[\begin{array}{lll}a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3\end{array}\right]\) is an adjoint of the matrix \(\left[\begin{array}{rrr}1 & 3 & 3 \\ 1 & 4 & 3 \\ 1 & 3 & 4\end{array}\right]\). The value of \(\frac{a_1+b_2+c_3}{b_1 a_2}\) is

The determinant of the matrix \(\left[\begin{array}{ccc}1 & 4 & 8 \\ 1 & 9 & 27 \\ 1 & 16 & 64\end{array}\right]\) is

If $A, B$ are two square matrices, such that $A B=A, B A=B$, then $(A+B)^7$ equals

If $A=\left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right]$ and $B=\left[\begin{array}{cc}\frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2}\end{array}\right]$, then $\left(B B^T A\right)^5$ is equal to