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If A is a square matrix, what is the necessary condition for the existence of its inverse?
If A is a square matrix, what is the necessary condition for the existence of its inverse?
A must be a non-singular matrix, i.e., its determinant |A| should not be zero.
What is the result of multiplying a matrix A with its inverse A⁻¹?
What is the result of multiplying a matrix A with its inverse A⁻¹?
The result is the identity matrix I.
If A and B are two invertible matrices of the same order, what can be said about the invertibility of AB?
If A and B are two invertible matrices of the same order, what can be said about the invertibility of AB?
AB is also an invertible matrix.
What is the effect of elementary row operations on the determinant of a matrix?
What is the effect of elementary row operations on the determinant of a matrix?
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If A is a symmetric matrix, what can be said about the matrix A + A′?
If A is a symmetric matrix, what can be said about the matrix A + A′?
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If A is a skew symmetric matrix, what can be said about the matrix A - A′?
If A is a skew symmetric matrix, what can be said about the matrix A - A′?
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What is the necessity of the matrix A to be a square matrix for the existence of its inverse?
What is the necessity of the matrix A to be a square matrix for the existence of its inverse?
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Can a non-singular matrix have a zero row or column?
Can a non-singular matrix have a zero row or column?
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What is the result of multiplying a matrix A with its transpose A′?
What is the result of multiplying a matrix A with its transpose A′?
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If A and B are two matrices, what is the condition for the existence of the product AB?
If A and B are two matrices, what is the condition for the existence of the product AB?
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