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 $A^{-1}$ using column transformations:$A=\left[\begin{array}{cc}2 & -3 \\-1 & 2\end{array}\right]$
→
Let * be a binary operation on Q - {-1} defined by a * b = a + b + ab for all a, b ∈ Q - {-1}. Then,
Find the identity element in Q − {−1}.
→
Diffrentiate the following w. r. t. x

$\sin ^{-1}\left(\frac{1-x^3}{1+x^3}\right)$

→
Find the cofactors of the elements for the matrix $\left[\begin{array}{ll}-1 & 2 \\ -3 & 4\end{array}\right]$
→
Form the differential equation by eliminating arbitrary constants from the relation
$y= Ae ^{ 5r }+ B e ^{- 5r \text {. }}$
→
Evalute the following integrals:
$\int\frac{\text{e}^{3\text{x}}}{\text{e}^{3\text{x}}+1}\text{dx}$
→
Evaluate: $\int x \log x d x$
→
Find the second order derivative of the following : $x^3+7 x^2-2 x-9$
→
If $\text{X}-\text{Y}=\begin{bmatrix}1&1&1\\1&1&0\\1&0&0\end{bmatrix}$ and $\text{X}+\text{Y}=\begin{bmatrix}3&5&1\\-1&1&4\\11&8&0\end{bmatrix},$ find X and Y.
→
Find the adjoint of the following matrices $:\left[\begin{array}{cc}2 & -3 \\ 3 & 5\end{array}\right]$
→