MtxProperties
Matrices  

Matrices  Introduction  Addition & Subtraction  Multiplication  Properties of Matrices  Inverse of a Matrix  Applications  Contribute  Answers 
Look at the following properties that you have noticed so far while doing Addition, Subtraction and Multiplication. 
 A_{2x3} + B_{2x3} = C_{2x3}
When we Add two matrices of the 'same order' (in this case they are 2x3) it gives another matrix of that same order (in this case a 2x3 matrix.)  A_{2x3}  B_{2x3} = C_{2x3}
When we Subtract two matrices of the 'same order' (in this case they are 2x3) it gives another matrix of that same order (in this case a 2x3 matrix).  Rectangular Matrices;
 A_{2x3} × B_{3x2} = C_{2x2}
When we Multiply a matrix of order a x b by a matrix of order b x c we get a matrix of order a x c.  B_{3x2} × A_{2x4} = D_{3x4}
When we Multiply a matrix of order b x a by a matrix of order a x c we get a matrix of order b x c.
 A_{2x3} × B_{3x2} = C_{2x2}
If you look at the above two cases, you will notice that in general
A x B is not equal to B x A.
 When do we get a square matrix as the answer?
 A_{2x3} × B_{3x2} = C_{2x2}
When we Multiply a matrix of order a x b by a matrix of order b x a we get a square matrix of order a x a.  A_{3x3} × B_{3x3} = C_{3x3}
When we Multiply a matrix of order a x a by a matrix of order a x a we get a square matrix of order a x a.
Write the order of the matrix that you get as the result of performing the given operation with the two given matrices.(Warning! You might not be able to perform the operation with the given matrices. In that case write "No Answer".
First matrix  Operation  Second matrix  Resultant matrix 

A_{3x2}  +  B_{3x2}  C_{?} 
A_{2x3}    B_{3x2}  C_{?} 
A_{3x2}  +  B_{2x3}  C_{?} 
A_{3x3}    B_{3x3}  C_{?} 
A_{2x3}  x  B_{3x3}  C_{?} 
A_{3x2}  x  B_{2x4}  C_{?} 
A_{2x3}  x  B_{2x3}  C_{?} 
A_{1x3}  x  B_{3x1}  C_{?} 
A_{2x3}  x  B_{2x3}  C_{?} 
A_{4x1}  x  B_{1x2}  C_{?} 
A_{1x2}    B_{2x3}  C_{?} 
A_{3x1}    B_{1x3}  C_{?} 
Multiplication of Matrices
