Answer
Verified
38.4k+ views
Hint: - In this question use the associative property of the matrix which is \[X\left( {YZ} \right) = \left( {XY} \right)Z\].
Given:
$AB = {\text{ }}B{\text{ }}..............\left( 1 \right),{\text{ }}BA = A...............\left( 2 \right)$
Now we have to find out the value of ${A^2} + {B^2}$
$ \Rightarrow {A^2} + {B^2} = AA + BB$
Now from equation (1) and (2) substitute the values of matrix B and A in above equation we have,
$ \Rightarrow {A^2} + {B^2} = A\left( {BA} \right) + B\left( {AB} \right)$
Now, from the associative property of matrix which is \[X\left( {YZ} \right) = \left( {XY} \right)Z\] we have,
$ \Rightarrow {A^2} + {B^2} = \left( {AB} \right)A + \left( {BA} \right)B$ (Associative property)
Now, again from equation (1) and (2) substitute the values of matrix AB and BA in above equation we have,
$ \Rightarrow {A^2} + {B^2} = BA + AB$
Now, again from equation (1) and (2) substitute the values of matrix AB and BA in above equation we have,
$ \Rightarrow {A^2} + {B^2} = A + B$
Hence, option (c) is the correct answer.
Note: -In these types of questions the key concept we have to remember is that always remember the properties of multiplication of matrix which is stated above then simplify the matrix according to given conditions then apply the associative property of matrix to get the required answer.
Given:
$AB = {\text{ }}B{\text{ }}..............\left( 1 \right),{\text{ }}BA = A...............\left( 2 \right)$
Now we have to find out the value of ${A^2} + {B^2}$
$ \Rightarrow {A^2} + {B^2} = AA + BB$
Now from equation (1) and (2) substitute the values of matrix B and A in above equation we have,
$ \Rightarrow {A^2} + {B^2} = A\left( {BA} \right) + B\left( {AB} \right)$
Now, from the associative property of matrix which is \[X\left( {YZ} \right) = \left( {XY} \right)Z\] we have,
$ \Rightarrow {A^2} + {B^2} = \left( {AB} \right)A + \left( {BA} \right)B$ (Associative property)
Now, again from equation (1) and (2) substitute the values of matrix AB and BA in above equation we have,
$ \Rightarrow {A^2} + {B^2} = BA + AB$
Now, again from equation (1) and (2) substitute the values of matrix AB and BA in above equation we have,
$ \Rightarrow {A^2} + {B^2} = A + B$
Hence, option (c) is the correct answer.
Note: -In these types of questions the key concept we have to remember is that always remember the properties of multiplication of matrix which is stated above then simplify the matrix according to given conditions then apply the associative property of matrix to get the required answer.
Recently Updated Pages
To get a maximum current in an external resistance class 1 physics JEE_Main
f a body travels with constant acceleration which of class 1 physics JEE_Main
If the beams of electrons and protons move parallel class 1 physics JEE_Main
If a wire of resistance R is stretched to double of class 12 physics JEE_Main
Let f be a twice differentiable such that fleft x rightfleft class 11 maths JEE_Main
Find the points of intersection of the tangents at class 11 maths JEE_Main
Other Pages
Differentiate between homogeneous and heterogeneous class 12 chemistry JEE_Main
Electric field due to uniformly charged sphere class 12 physics JEE_Main
A point charge q placed at the point A is A In stable class 12 physics JEE_Main
The reaction of Zinc with dilute and concentrated nitric class 12 chemistry JEE_Main
Formula for number of images formed by two plane mirrors class 12 physics JEE_Main
Excluding stoppages the speed of a bus is 54 kmph and class 11 maths JEE_Main