Download App

Algebra of Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsAlgebra of Matrices2 Marks
Question
If $\text{A}=\begin{bmatrix}2&1&4\\4&1&5 \end{bmatrix}$ and $\text{B}=\begin{bmatrix}3&-1\\2&2\\1&3\end{bmatrix}.$ Write the order of AB and BA.
✓

Answer

Order of $A=2 \times 3$
Order of $B=3 \times 2$
So,
$\mathrm{A}_{2 \times 3} \times \mathrm{B}_{3 \times 2}$ has order $=2 \times 2$
$\mathrm{B}_{3 \times 2} \times \mathrm{A}_{2 \times 3}$ has order $=3 \times 3$
Hence,
Order of $A B=2 \times 2$
Order of $B A=3 \times 3$

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 Algebra of Matrices→Algebra of Matrices — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Given two independent events A and B such that P(A) = 0.3 and P(B) = 0.6. Find
$\text{P}(\text{A}\cap\overline{\text{B}})$
→
Is it true that $x = e^{\log x}$ for all real $x?$
→
A matrix of order $3 \times 3$ has determinant $2.$ What is the value of $|A(3I)|,$ where I is the identity matrix of order $3 \times 3.$
→
$A, B, C$ are three non-null square matrices of the same order, write the condition on A such that $AB = AC ⇒ B = C$.
→
If x and y are connected parametrically by the equation $x = a\sec \theta,$ $y = b\tan \theta $, without eliminating the parameter, find $\frac{{dy}}{{dx}}$.
→
Write the value of $\hat{\text{i}}\times\big(\hat{\text{j}}+\hat{\text{k}}\big)+\hat{\text{j}}\times\big(\hat{\text{k}}+\hat{\text{i}}\big)+\hat{\text{k}}\times\big(\hat{\text{i}}+\hat{\text{j}}\big).$
→
If $\vec{\text{a}}$ and $\vec{\text{b}}$ are two vectors such that $\big|\vec{\text{a}}\big|=4,\big|\vec{\text{b}}\big|=3$ and $\vec{\text{a}}.\vec{\text{b}}=6,$ find the angle between $\vec{\text{a}}$ and $\vec{\text{b}}$.
→
For the binary operation multiplication modulo $5 (\times _5)$ defined on the set $S = \{1, 2, 3, 4\}.$ Write the value of $(3 \times _5 4^{-1})^{−1}$​​​​​​​
→
Evaluate $\begin{vmatrix}4785&4787\\4789&4791\end{vmatrix}$
→
Let $f, g : R \rightarrow R$ be defined by $f(x) = 2x + 1$ and $g(x) = x^2 - 2$ for all $x \in R$, respectively. Then, find gof.
→