Matrices — Class 12 Maths Solution

exemplar tf TrueFalse NCERT,Exemp,Q.no.101,Page 64

Question

${(AB)^{ - 1}} = {A^{ - 1}} \cdot {B^{ - 1}}$, where A and B are invertible matrices satisfying commutative property with respect to multiplication.

Correct Answer True

Step-by-step Solution

As we know,, if A and B are invertible matrices of the same order, then
${(AB)^{ - 1}} = {(BA)^{ - 1}}$

Here, ${(AB)^{ - 1}} = {(AB)^{ - 1}}$

$\Rightarrow$ ${B^{ - 1}}{A^{ - 1}} = {A^{ - 1}}{B^{ - 1}}$

[since, A and B are satisfying commutative property with respect to multiplications].

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