List of top Mathematics Questions on Invertible Matrices asked in KEAM

If \(X = A^{-1}B,\) Where \(A = \left[ \begin{array}{cc}1 & -1 2 & 1 \end{array} \right],B = \left[ \begin{array}{c}3 6 \end{array} \right]\) and \(X = \left[ \begin{array}{c}x_{1} x_{2} \end{array} \right],\) then \(x_{1} + x_{2} =\)

If $\begin{pmatrix} e & f \\ g & h \end{pmatrix}$ is the inverse of the matrix $\begin{pmatrix} a & b \\ c & d \end{pmatrix}$ where $ad - bc = 1$, then $g$ equals

If \[ \begin{pmatrix} a & b \\ c & d \end{pmatrix} \] is the inverse of the matrix \[ \begin{pmatrix} 1 & 5 \\ 7 & -3 \end{pmatrix}, \] then \( d \) equals

If \( A=\begin{bmatrix}2x & 0 x & x \end{bmatrix} \) and \( A^{-1}=\begin{bmatrix}1 & 0 -1 & 2 \end{bmatrix} \), find \(x\)

If \( A = \begin{bmatrix} 1 & 2 & 3 0 & 1 & 4 5 & 6 & 0 \end{bmatrix} \), then the sum of the diagonal elements of \( A^{-1} \) is

If \( A = \begin{bmatrix} 2 & 1 3 & 2 \end{bmatrix} \), then \( A^{-1} \) is

If \( A = \begin{bmatrix} 1 & 2 & 3 0 & 1 & 4 5 & 6 & 0 \end{bmatrix} \), then the sum of the diagonal elements of \( A^{-1} \) is

If \( A = \begin{bmatrix} 2 & 1 3 & 2 \end{bmatrix} \), then \( A^{-1} \) is

If \( A=\begin{bmatrix}2x & 0 x & x \end{bmatrix} \) and \( A^{-1}=\begin{bmatrix}1 & 0 -1 & 2 \end{bmatrix} \), find \(x\)

If \( U = \begin{bmatrix} \frac{1}{\sqrt{2}} & -\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} \end{bmatrix} \), then \( U^{-1} \) is:

If \( A = \begin{bmatrix} 0 & -1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & -1 \end{bmatrix} \), then \( A^{-1} \) is: