If A and B are square matrices of the same or | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) We are given the expression $(B^{-1}AB)^5$. This can be written as the product of $5$ terms: $(B^{-1}AB)^5 = (B^{-1}AB)(B^{-1}AB)(B^{-1}AB)(B^{-1}

Vedclass · Accepted Answer

$B^{-1}A^5B$

Vedclass · Answer

(C) We are given the expression $(B^{-1}AB)^5$. This can be written as the product of $5$ terms: $(B^{-1}AB)^5 = (B^{-1}AB)(B^{-1}AB)(B^{-1}AB)(B^{-1}AB)(B^{-1}AB)$. Since matrix multiplication is associative,we can group the terms as: $= B^{-1}A(BB^{-1})A(BB^{-1})A(BB^{-1})A(BB^{-1})AB$. Since $BB^{-1} = I$ (the identity matrix),the expression simplifies to: $= B^{-1}A(I)A(I)A(I)A(I)AB$. $= B^{-1}AAAAAB$. $= B^{-1}A^5B$.

If $A$ and $B$ are square matrices of the same order and $|B| \neq 0$,then $(B^{-1}AB)^5$ is equal to

Similar Questions

If ${I_3}$ is the identity matrix of order $3$,then ${I_3}^{-1}$ is

If $A = \begin{bmatrix} x & 1 \\ 1 & 0 \end{bmatrix}$ and $A = A^{-1}$,then $x = \dots$

If ${A^2} - A + I = 0$,then ${A^{-1}} = $

If $A$ and $B$ are square matrices of order $3$ such that $|A|=2$ and $|B|=4$,then $|A(\operatorname{adj} B)| = \dots$

If $A$ is a non-singular matrix,then $A(\text{adj } A) =$

Vedclass Test Series

Exam Paper Generator

Online Exam Module