B18 said:Yes I can see that. But I don't think we can use inverses or inverse properties on this proof because CA and AD are not both the same size matrices.
Ok, i think I've got this one nailed down.Dick said:You don't have to. Think about the matrix CAD. Use the associative property.
B18 said:Ok, i think I've got this one nailed down.
CA=In
CAD=InD
C(AD)=D [identity matrix times D is still the matrix D]
since AD=Im
we have C(Im)=D
C=D [identity matrix times C is still the matrix C]
Two matrices are equal if they have the same dimensions and each corresponding element in the matrices are equal. This means that they have the same number of rows and columns, and the values in each position within the matrices are the same.
To prove two matrices are equal, you must show that they have the same dimensions and that each corresponding element is equal. This can be done by comparing each element in the first matrix to the corresponding element in the second matrix and showing that they are equal in value.
No, two matrices with different dimensions cannot be equal. In order for two matrices to be equal, they must have the same number of rows and columns. If the dimensions are different, then the matrices are not equal.
No, two matrices with the same dimensions but different elements cannot be equal. In order for two matrices to be equal, each corresponding element must have the same value. If the elements are different, then the matrices are not equal.
One shortcut to proving two matrices are equal is to show that their difference is equal to the zero matrix. If the difference between the two matrices is the zero matrix, then they must be equal. Another shortcut is to use the property that if two matrices are equal, then their transpose matrices are also equal.