Download App

Determinants — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDeterminants2 Marks
Question
If A and B are non-singular matrices of the same order, write whether AB is singular or non-singular.
✓

Answer

Let A & B be non-singular matrices of order n.
A ≠ 0 and B ≠ 0 By definition.
Since they are of same order, AB = AB, AB = 0 if either A = 0 or B = 0 But it is not the case here. Thus, AB is non-zero and AB is non-singular matrix.

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 Determinants→Determinants — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Find the expected number of boys in a family with 8 children, assuming the sex distribution to be equally probable.
→
Write converse, inverse and contrapositive of the following statements. If $x < y$ then $x^2 < y^2 (x, y \in R)$
→
If $\vec{\text{a}}=3\hat{\text{i}}-\hat{\text{j}}-4\hat{\text{k}},\ \vec{\text{b}}=-2\hat{\text{i}}+4\hat{\text{j}}-3\hat{\text{k}}$ and $\vec{\text{c}}=\hat{\text{i}}+2\hat{\text{j}}-\hat{\text{k}}$, find $\big|3\vec{\text{a}}-2\vec{\text{b}}+4\vec{\text{c}}\big|$.
→
Find the approximate values of:

$\log _{10}(1016)$, given that $\log _{10} e=0.4343$

→
Evaluate the following integrals:$\int^\limits{2\pi}_{0}|\sin\text{x}|\text{dx}$
→
The displacement of a particle at time $t$ is given by $s=2 t^3-5 t^2+4 t-3$. Find the time when the acceleration is $14 \mathrm{ft} / \mathrm{sec}^2$, the velocity and the displacement at that time.
→
If two events A and B are such that $\text{P}(\overline{\text{A}})=0.3,\text{P(B)}=0.4$ and $\text{P}(\text{A}\cap\overline{\text{B}})=0.5$ find $\text{P}\Big(\frac{\text{B}}{\overline{\text{A}}\cap\overline{\text{B}}}\Big).$
→
Find the adjoint of matrix $A=\left[\begin{array}{ll}6 & 5 \\ 3 & 4\end{array}\right]$
→
Write the identity element for the binary operation * on the set $R _0$ of all non-zero real numbers by the rule $a \times b=\frac{a b}{2}$ for all $a, b \in R_0$.
→
Find $' k \ '$ if the sum of slopes of lines represented by equation $x^2+k x y-3 y^2=0$ is twice their product.
→