A, B, C are three non-null square matrices of the same order, wri… - Vidyadip

Question

$\text{A, B, C}$ are three non$-$null square matrices of the same order, write the condition on $A$ such that $AB = AC$ $\Rightarrow B = C.$

✓

Answer

Consider $AB = AC$.
On multiplying both sides by $A^{-1},$ we get $AA^{-1}B = AA^{-1}$
$\Rightarrow IB = IC\ [$Because $AA^{-1} = I$ where $I$ is the identity matrix$]$
$\Rightarrow B = C$
Therefore, the required condition is $A$ must be invertible or $|\text{A}|\neq0$.

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 "2 Marks Questions" from DETERMINANTS→DETERMINANTS — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Write Minors and Cofactors of the elements of following determinant: $\begin{vmatrix}a&c\\b&d\end{vmatrix}$

If A is a square matrix such that A (adj A) = 5I, where I denotes the identity matrix of the same order. Then, find the value of |A|.

Evaluate: $\begin{vmatrix}\cos15^\circ&\sin15^\circ\\\sin75^\circ&\cos75^\circ\end{vmatrix}$

A particle moves along the curve $6y = x^3 + 2$. Find the points on the curve at which the $y\ -$ coordinate is changing $8$ times as fast as the $x\ –$ coordinate.

Construct a $3 \times 4$ matrix $A = [a_{ij}]$ whose element $a_{ij}$ are given by:
$\text{a}_\text{ij}=\frac{1}{2}|-3\text{i}+\text{j}|$

Find the values of the following:
$\tan^{-1}\Big\{2\cos\Big(2\sin^{-1}\frac{1}{2}\Big)\Big\}$

Evaluate the following integrals:
$\int\frac{1}{1+\cos2\text{x}}\text{dx}$

Evaluate the definite integral$\int_{0}^{\frac{\pi}{2}} \cos 2 x d x$

A stone is dropped into a quiet lake and waves move in circles at the speed of 5 cm/s. At the instant when the radius of the circular wave is 8 cm, how fast is the enclosed area increasing?

Write a unit vector perpendicular to $\hat{\text{i}}+\hat{\text{j}}$ and $\hat{\text{j}}+\hat{\text{k}}.$