Discuss: Square Root of Matrices A square root of a matrix is a matrix with the property that . (This is the same definition as for a square root of a number.) Find as many square roots as you can of each matrix:
[Hint: If , write the equation that , , and would have to satisfy if is the square root of the given matrix.]
The square root of the matrices and .
Two matrices and can be multiplied if and only if the number of columns in is same as the number of rows in .
If is an matrix and an matrix, then their product in the matrix .
Consider the matrix .
Let be the square root of the matrix .
Therefore, the elements of is calculated below.
Compare the obtained results with the given matrix.
The following equations are formed from the above obtained results.
Solving the above equations results , , and .
Therefore, the square root of the matrix is or .
Consider the matrix
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