Is it possible to have the product of two matrices?

Example 9: Multiplying Two Matrices Find B A \displaystyle BA BA.

Can there be a non zero matrix whose square is zero matrix?

Yes. Nilpotent matrix of any order and of index 2. There is a matrix called Nilpotent matrix (which is in JEE syllabus not in boards). A matrix whose nth power is equal to zero is called Nilpotent matrix.

Are all zero matrices equal?

A matrix is said to be a zero matrix if all its entries are 0. Hence we can say that [000000] is a zero Matrix. But if we have two zero matrices of different order then the matrices are not equal. For example consider [000000] and [00] are both zero matrices but not equal.

Can you square a zero matrix?

From the zero matrix notation examples above, notice that these matrices can come in any size and dimension combination, and they are not necessarily square matrices. Thus, both of these two types of matrices are what we call a zero trace matrix.

What is nonzero square matrix?

A non-singular matrix is a square one whose determinant is not zero. Thus, a non-singular matrix is also known as a full rank matrix. For a non-square [A] of m × n, where m > n, full rank means only n columns are independent.

Can the product of two non zero matrices be a zero matrix?

. i.e. the product of the matrix with a null matrix is always a null matrix. (g) If AB = 0 (It does not mean that A = 0 or B = 0, again the product of two non-zero matrices may be a zero matrix).

Is it possible for a matrix to be a null matrix?

Yes it is possible. A null matrix or a zero matrix is a matrix in which all its elements are 0. Neither A nor B is a null matrix since they have non-zero elements. This is null matrix, a 1×1 matrix where all the elements are 0.

Is it possible to compare two matrices with different numbers?

Yes it is possible. A null matrix or a zero matrix is a matrix in which all its elements are 0. Neither A nor B is a null matrix since they have non-zero elements. This is null matrix, a 1×1 matrix where all the elements are 0. Yes, it is possible. You can’t always compare matrices to individual numbers.

What is the product of A and B in matrices?

If A and B be any two matrices, then their product AB will be defined only when the number of columns in A is equal to the number of rows in B. AB e BA. AB  = BA.