Question

$If space straight A equals open square brackets table row 2 cell negative 1 end cell 3 row cell negative 3 end cell 2 0 row 5 1 cell negative 1 end cell end table close square brackets comma straight B equals space open square brackets table row cell negative 3 end cell 2 cell negative 1 end cell row 0 5 2 row 1 cell negative 2 end cell cell negative 1 end cell end table close square brackets space then find space AB space and space BA. space Is space AB equals BA ? space What space conclusion space do space you space draw$

Solution

straight A space equals open square brackets table row 2 cell negative 1 end cell 3 row cell negative 3 end cell 2 0 row 5 1 1 end table close square brackets comma space straight B equals open square brackets table row cell negative 3 end cell 2 cell negative 1 end cell row 0 5 2 row 1 cell negative 2 end cell 1 end table close square brackets AB equals space open square brackets table row 2 cell negative 1 end cell 3 row cell negative 3 end cell 2 0 row 5 1 cell negative 1 end cell end table close square brackets open square brackets table row cell negative 3 end cell 2 cell negative 1 end cell row 0 5 2 row 1 cell negative 2 end cell 1 end table close square brackets equals open square brackets table row cell left parenthesis 2 right parenthesis left parenthesis negative 3 right parenthesis plus left parenthesis negative 1 right parenthesis left parenthesis 0 right parenthesis plus left parenthesis 3 right parenthesis left parenthesis 1 right parenthesis end cell cell space left parenthesis 2 right parenthesis left parenthesis 2 right parenthesis plus left parenthesis negative 1 right parenthesis left parenthesis 5 right parenthesis plus left parenthesis 3 right parenthesis left parenthesis negative 2 right parenthesis end cell cell space space left parenthesis 2 right parenthesis left parenthesis negative 1 right parenthesis plus left parenthesis negative 1 right parenthesis left parenthesis 2 right parenthesis plus left parenthesis 3 right parenthesis left parenthesis 1 right parenthesis end cell row cell left parenthesis negative 3 right parenthesis left parenthesis negative 3 right parenthesis plus left parenthesis 2 right parenthesis left parenthesis 0 right parenthesis plus left parenthesis 0 right parenthesis left parenthesis 1 right parenthesis space end cell cell left parenthesis negative 3 right parenthesis left parenthesis 2 right parenthesis plus left parenthesis 2 right parenthesis left parenthesis 5 right parenthesis plus left parenthesis 0 right parenthesis left parenthesis negative 2 right parenthesis end cell cell space space left parenthesis negative 3 right parenthesis left parenthesis negative 1 right parenthesis plus left parenthesis 2 right parenthesis left parenthesis 2 right parenthesis plus left parenthesis 0 right parenthesis left parenthesis 1 right parenthesis end cell row cell left parenthesis 5 right parenthesis left parenthesis negative 3 right parenthesis plus left parenthesis 1 right parenthesis left parenthesis 0 right parenthesis plus left parenthesis negative 1 right parenthesis left parenthesis 1 right parenthesis end cell cell space left parenthesis 5 right parenthesis left parenthesis 2 right parenthesis plus left parenthesis 1 right parenthesis left parenthesis 5 right parenthesis plus left parenthesis negative 1 right parenthesis left parenthesis negative 2 right parenthesis space end cell cell space space space left parenthesis 5 right parenthesis left parenthesis negative 1 right parenthesis plus left parenthesis 1 right parenthesis left parenthesis 2 right parenthesis plus left parenthesis negative 1 right parenthesis left parenthesis 1 right parenthesis end cell end table close square brackets equals open square brackets table row cell negative 6 plus 0 plus 3 end cell cell 4 minus 5 minus 6 end cell cell negative 2 minus 2 plus 3 end cell row cell 9 plus 0 plus 0 end cell cell negative 6 plus 10 plus 0 end cell cell 3 plus 4 plus 0 end cell row cell negative 15 plus 0 minus 1 end cell cell 10 plus 5 plus 2 end cell cell negative 5 plus 2 minus 1 end cell end table close square brackets equals open square brackets table row cell negative 3 end cell cell negative 7 end cell cell negative 1 end cell row 9 4 7 row cell negative 16 end cell 17 cell negative 4 end cell end table close square brackets also space BA equals open square brackets table row cell negative 3 end cell 2 cell negative 1 end cell row 0 5 2 row 1 cell negative 2 end cell 1 end table close square brackets open square brackets table row 2 cell negative 1 end cell 3 row cell negative 3 end cell 2 0 row 5 1 cell negative 1 end cell end table close square brackets equals open square brackets table row cell negative 6 minus 6 minus 5 end cell cell 3 plus 4 minus 1 end cell cell negative 9 plus 0 plus 1 end cell row cell 0 minus 15 plus 10 end cell cell 0 plus 10 plus 2 end cell cell 0 plus 0 minus 2 end cell row cell 2 plus 6 plus 5 end cell cell negative 1 minus 4 plus 1 end cell cell 3 minus 0 minus 1 end cell end table close square brackets equals open square brackets table row cell negative 17 end cell 6 cell negative 8 end cell row cell negative 5 end cell 12 cell negative 2 end cell row 13 cell negative 4 end cell 2 end table close square brackets therefore space AB space not equal to space BA

We conclude that multiplication of matrices A and B is not commutative.

For Daily Free Study Material Join wiredfaculty

Matrices

Some More Questions From Matrices Chapter

If a matrix has 8 elements, what arc the possible orders it can have ?

If a matrix has 24 elements, what are the possible orders it can have? What, if it has 13 elements?

If a matrix has 18 elements, what are the possible orders it can have? What, if it has 5 elements?

If a matrix A has 12 elements, what arc the possible orders it can have 7 What if it has 7 elements ?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction