If A is a square matrix of order 3, then the product of A and its transpose is (a) unit matrix (

step 1 So in the given question we are told that A is a square matrix, A is a squared matrix, a square

If A is a square matrix of order 3, then the product of A...

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Key Concepts

Matrix Transpose

The transpose of a matrix involves swapping its rows with its columns. This operation is fundamental in linear algebra and influences how matrices interact, especially during multiplication.

Matrix Multiplication

Matrix multiplication is a standard operation in linear algebra where rows of the first matrix are combined with columns of the second. The product's properties depend on the matrices involved, particularly when one of them is a transpose.

Symmetric Matrix

A symmetric matrix is defined as a matrix that is equal to its own transpose. The product of any matrix and its transpose, such as A * A^T, is always symmetric because the order of multiplication reverses under transposition, yielding the same matrix.

Orthogonal Matrix

An orthogonal matrix is a special type of square matrix whose rows and columns form an orthonormal set. For such matrices, A * A^T results in the identity matrix. However, this is a particular case and does not hold for all matrices.

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