List of top Mathematics Questions on Inverse of a Matrix

If $ A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} $, then $ A^{-1} $ is:

For a square matrix $A$, $(3A)^{-1}$ is

A store has been selling calculators at Rs. 350 each. A market survey indicates that a reduction in price ($ p $) of calculators increases the number of units ($ x $) sold. The relation between the price and quantity sold is given by the demand function:

\[ p = 450 - \frac{x}{2}. \]

Based on the above information, answer the following questions:

If $ y = \cos^3(\sec^2 2t) $, find $ \frac{dy}{dt} $.

The integrating factor of the differential equation $ (x + 2y^2) \frac{dy}{dx} = y \, (y > 0) $ is:

If $ A = \begin{bmatrix} 2 & 1 \\ -4 & -2 \end{bmatrix} $, then the value of $ I - A + A^2 - A^3 + \ldots $ is:

Given that $ A^{-1} = \frac{1}{7} \begin{bmatrix} 2 & 1 \\ -3 & 2 \end{bmatrix} $, matrix $ A $ is:

The integrating factor of the differential equation $ \frac{dy}{dx} + \frac{2}{x} y = 0 $, $ (x \neq 0) $ is:

The value of $ \int_{0}^{\pi} \tan^2 \left( \frac{\theta}{3} \right) d\theta $ is:

Derivative of $ x^2 $ with respect to $ x^3 $, is: