If A is matrix of order m n and B is a matrix such that A B and B A are both defined, then order of matrix B is

Let A = m n and B = p q = q p Now, A B is defined, so n = q and B A is also defined, so p = m Order of B = n m and order of B = m n

Matrices — Class 12 Maths Solution

exemplar objective MCQ NCERT,Exemp,Q.no.62,Page 61

Question

If A is matrix of order $m \times n$ and B is a matrix such that $A{B^\prime }$ and ${B^\prime }A$ are both defined, then order of matrix B is

Step-by-step Solution

Let $A = {\left[ {{a_{ij}}} \right]_{m \times n}}$ and $B = {\left[ {{b_{ij}}} \right]_{p \times q}}$

$\therefore$ ${B^\prime } = {\left[ {{b_{jj}}} \right]_{q \times p}}$
Now, $A{B^\prime }$ is defined, so $n = q$

and ${B^\prime }A$ is also defined, so $p = m$

$\therefore$ Order of ${B^\prime } = {\left[ {{b_{ji}}} \right]_{n \times m}}$

and order of $B = {\left[ {{b_{ij}}} \right]_{m \times n}}$

NCERT & Exemplar solution for CBSE Class 12 Mathematics, Matrices. Curated by Sachin Sharma. Free for all students.