10 Questions
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?
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?
AB is also an invertible matrix.
What is the effect of elementary row operations on the determinant of a matrix?
The determinant remains unchanged.
If A is a symmetric matrix, what can be said about the matrix A + A′?
A + A′ is a symmetric matrix.
If A is a skew symmetric matrix, what can be said about the matrix A - A′?
A - A′ is a skew symmetric matrix.
What is the necessity of the matrix A to be a square matrix for the existence of its inverse?
A must be a square matrix to have an inverse, as the number of equations must be equal to the number of variables.
Can a non-singular matrix have a zero row or column?
No, a non-singular matrix cannot have a zero row or column.
What is the result of multiplying a matrix A with its transpose A′?
The result is a symmetric matrix.
If A and B are two matrices, what is the condition for the existence of the product AB?
The number of columns of A must be equal to the number of rows of B.
Learn about the rules and examples of matrix addition and scalar multiplication. Understand the importance of matrix order in these operations.
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