If A=[1 0 0 -1] and B=[0 1 1 0], then

Question

If A=[1 0 0 -1] and B=[0 1 1 0], then (A) A B=[0 -1 1 0] (B) B A=[0 1 -1 0] (C) A B=B A (D) A B ≠ B A

Tardigrade Admin · Accepted Answer

If A=[1 0 0 -1] and B=[0 1 1 0], then A B=[0 1 -1 0] and B A=[0 -1 1 0] Clearly, A B ≠ B A Thus, matrix multiplication is not commutative. This shows that even if A B and B A are of same order, then they may not be same

Q. If $A = [10 0 - 1]$ and $B = [0110]$ , then

$A B = [01 - 1 0]$

$B A = [0 - 1 10]$

$A B = B A$

$A B \neq = B A$

If $A = [10 0 - 1]$ and $B = [0110]$ , then $A B = [0 - 1 10]$ and $B A = [01 - 1 0]$ Clearly, $A B \neq = B A$
Thus, matrix multiplication is not commutative.
This shows that even if $A B$ and $B A$ are of same order, then they may not be same

Q. If A=[10​0−1​] and B=[01​10​], then

AB=[01​−10​]

BA=[0−1​10​]

AB=BA

AB=BA