If it is not a square matrix.
You cannot invert a square matrix if it is singular. That means that at least one of the rows of the matrix can be expressed as a linear combination of the other rows.
A simple test is that a matrix cannot be inverted if its determinant is zero.
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An idempotent matrix is a matrix which gives the same matrix if we multiply with the same. in simple words,square of the matrix is equal to the same matrix. if M is our matrix,then MM=M. then M is a idempotent matrix.
Reduced matrix is a matrix where the elements of the matrix is reduced by eliminating the elements in the row which its aim is to make an identity matrix.
If an identity matrix is the answer to a problem under matrix multiplication, then each of the two matrices is an inverse matrix of the other.
Each number in the matrix is called an element of the matrix
To solve simultaneous equations using matrices, you first need to represent the equations in matrix form. Create a matrix equation by combining the coefficients of the variables and the constants on one side, and the variables on the other side. Then, use matrix operations to manipulate the matrices to solve for the variables. Finally, you can find the values of the variables by performing matrix multiplication and inversion to isolate the variables.