Can the product of two nonzero matrices be zero matrix?

Can the product of two nonzero matrices be zero matrix?

1. The product of two non-zero matrices can never be identity matrix. The product of two non-zero matrices can never be zero matrix.

Is it true product of two matrix is a zero matrix when at least one of them is a zero matrix justify?

After multiplying two non-zero matrices, we get a zero matrix. Hence, to get the answer, we had considered two non-zero matrices and we got the product as a zero matrix. Thus, option (C), it is not necessary that either A is zero matrix or B is zero matrix, is correct.

Can a nonzero matrix contain zeros?

If you think this idea more in depth, you will realize that any non zero matrix cannot have a rank smaller than one, in other words, in order for any matrix to have a rank of zero, it must contain all zero elements inside, and so, our conclusion is that only zero matrices have a rank of zero.

What matrix is equal to zero?

4. A null (zero) matrix is a matrix in which all elements are zero.

What is a nonzero matrix?

A nonzero matrix is a matrix that has at least one nonzero element. A nonzero vector is a vector with magnitude not equal to zero.

What is the product of two non-zero consecutive whole number?

We know that, among any two consecutive numbers one number is bound to be even, and product of any number with even number is even. Let two non-zero consecutive whole numbers are \(1\) and \(2\). Now, the product of two non-zero consecutive whole numbers \(=1\times2=2\), which is an even number.

What is a non zero matrix?

Not equal to zero. A nonzero matrix is a matrix that has at least one nonzero element. A nonzero vector is a vector with magnitude not equal to zero.

What is nonzero matrix with example?

12 For a matrix A, the number of non-zero rows in E(A) is the rank of A, written r(A). For example, the matrix A of Example 11.5. 7 has two non-zero rows and so r(A) = 2.

Are two zero matrices equal?

Now if we have a zero matrix of the same order then definitely we can say that the two matrices are equal.

What is the non-zero vector?

A non-zero vector is one with at least one non-zero entry, at least in Rn or Cn. In general, a non-zero vector is one that is not the identity element for addition of the vector space in question.