Download App

Adjoint and Inverse of a Matrix — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsAdjoint and Inverse of a Matrix2 Marks
Question
If A is a non-singular square matrix such that $\text{A}^{-1}=\begin{bmatrix} 5 & 3 \\ -2 & -1 \end{bmatrix},$ then find $(A^T)^{-1}$.
✓

Answer

For any invertible matrix A. $(A^T)^{-1} = (A^{-1})^T$ We have $\text{A}^{-1}=\begin{bmatrix} 5 & 3 \\ -2 & -1 \end{bmatrix}$$\Rightarrow(\text{A}^\text{T})^{-1}=\begin{bmatrix} 5 & -2 \\ 3 & -1 \end{bmatrix}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the Following Question.(2 Marks)" from Adjoint and Inverse of a Matrix→Adjoint and Inverse of a Matrix — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

A random variable $X \sim N(0,1)$. Find $P(X>0)$ and $P(X<0)$
→
A unit vector $\vec{\text{r}}$ makes angles $\frac{\pi}3\text{ and }\frac{\pi}2$ with $\hat{\text{j}}\text{ and } \hat{\text{k}}$ respectively and an acute angle $\theta$ with $\hat{\text{i}}$. Find $\theta$.
→
A bag contains $4$ white balls and $2$ black balls. Another contains $3$ white balls and $5$ black balls. If one ball is drawn from each bag, find the probability that,
One is while and one is black.
→
If f, g : R → R be two functions defined as f(x) = |x| + x and g(x) = |x| – x, $\forall\ \text{x}\in\text{R}.$ Then find fog and gof. Hence find fog(-3), fog(5) and gof(-2).
→
Solve the following differential equations:

$\log \left(\frac{d y}{d x}\right)=2 x+3 y$

→
If $X \sim B(n, p)$ with $n=10, p=0.4$, then find $E\left(X^2\right)$.
→
Find the derivative of the inverse of the following functions, and also fid their value at the points indicated against them :
If $f(x)=x^3+x-2$, find $\left(f^{-1}\right)^{\prime}(0)$
Question is modified.
If $f(x)=x^3+x-2$, find $\left(f^{-1}\right)^{\prime}(-2)$.
→
Using rules in logic, prove the following : ~p ∧ q ≡ (p ∨ q) ∧ ~p
→
Show that the vectors $4 \hat{i}+13 \hat{j}-18 \hat{k}, \hat{i}-2 \hat{j}+3 \hat{k}$ and $2 \hat{i}+3 \hat{j}-4 \hat{k}$ are coplanar.
→
Evaluate the following:
$\sec^{-1}\Big\{\sec\Big(-\frac{7\pi}{3}\Big)\Big\}$
→