UPES B.Tech Admissions 2025
ApplyRanked #46 among universities in India by NIRF | Highest CTC 50 LPA | 100% Placements
Multiplication of two matrices, Properties of Matrix Multiplication is considered one of the most asked concept.
47 Questions around this concept.
If then which one of the following statements is not correct ?
If then adj is equal to :
Let .The only correct statement about the matrix A is
New: Crack JEE Main 2025 - Join Our Free Crash Course Now!
JEE Main 2025: Sample Papers | Syllabus | Mock Tests | PYQs | Video Lectures
JEE Main 2025: Preparation Guide | High Scoring Topics | Study Plan 100 Days
If A and B are square matrices of size n x n such that then which of the following will be always true?
Let If u1 and u2 are column matrices such that
then u1 + u2 is equal to :
Consider the matrix $f(x)=\left[\begin{array}{ccc}\cos x & -\sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1\end{array}\right]$
Given below are two statements :
Statement I : $f(-x)$ is the inverse of the matrix $f(x)$.
Statement II : $\mathrm{f}(\mathrm{x}) \mathrm{f}(\mathrm{y})=\mathrm{f}(\mathrm{x}+\mathrm{y})$.
In the light of the above statements, choose the correct answer from the options given below:
Matrix multiplication:
Product AB can be found if the number of columns in matrix A and the number of rows in matrix B are equal. Otherwise, multiplication AB is not possible.
i) AB is defined only if col(A) = row(B)
ii) BA is defined only if col(B) = row(A)
If
For examples
Properties of matrix multiplication:
i) Multiplication may or may not be commutative, so AB may or may not be equal to BA.
ii) Matrix multiplication is associative, meaning A(BC) = (AB)C
iii) Matrix multiplication is distributive over addition, mean A(B+C) = AB + AC and (B+C)A = BA + CA
iv) If matrix multiplication of two matrices gives null matrix then it doesn’t mean that any of those two matrices was a null matrix.
So AB = O ⇏ A = O or B = O.
v) Cancellation law in matrix multiplication doesn’t hold, means AB = AC ⇏ B = C
vi) Matrix multiplication A x A is represented by A2. Thus, A・A・A・A……...n times = An.
vii) if A is m x n matrix then, .
"Stay in the loop. Receive exam news, study resources, and expert advice!"