List of top Mathematics Questions on Invertible Matrices asked in COMEDK UGET

If \( A = \begin{bmatrix} 4 & \lambda & -3 0 & 2 & 5 1 & 1 & 3 \end{bmatrix} \), then \( A^{-1} \) exists if:

Kiran purchased 3 pencils, 2 notebooks and one pen for INR 41. From the same shop Manasa purchased 2 pencils, one notebook and 2 pens for INR 29, while Shreya purchased 3 pencils, 2 notebooks and 2 pens for INR 44. The above situation can be represented in matrix form as \( AX = B \). Then \( \text{adj}(A) \) is equal to

The cost of 4 kg onion, 3 kg wheat and 2 kg rice is INR 500.
The cost of 1 kg onion, 2 kg wheat and 3 kg rice is INR 300.
The cost of 6 kg onion, 2 kg wheat and 3 kg rice is INR 575.
The above situation can be represented in matrix form as \( AX = B \). Then \( |5A^{-1}| = \)

For two matrices \(A\) and \(B\), given that \( A^{-1} = \frac{1}{8}B \) then inverse of \( (8A) \) is