Symmetric Matrix Calculator
Select the size of the square matrix and enter its elements to check if it is symmetric.
Quick Examples
Solved Exercises
The following are examples of problems solved by the calculator.
Exercise 1
Determine if the following matrix is symmetric:
$$ \displaystyle A = \begin{bmatrix} 1 & 2 & 3 \\[0.5em] 2 & 4 & -5 \\[0.5em] 3 & -5 & 6 \end{bmatrix} $$
Result
The given matrix is symmetric. This is because it is equal to its transpose.
Original matrix:
Transposed matrix:
To see this in detail, check the matrix transpose calculator.
Exercise 2
Check if the matrix is symmetric:
$$ \displaystyle A = \begin{bmatrix} -1 & 0 & 2 \\[0.5em] 4 & -3 & 5 \\[0.5em] 1 & 1 & -2 \end{bmatrix} $$
Result
The provided matrix is not symmetric, as it is not equal to its transpose.
Original matrix:
Transposed matrix:
Exercise 3
Verify if the following matrix is symmetric:
$$ \displaystyle A = \begin{bmatrix} 1 & 2 & 3 & 4 \\[0.5em] 2 & 0 & 5 & 6 \\[0.5em] 3 & 5 & -1 & 7 \\[0.5em] 4 & 6 & 7 & 8 \end{bmatrix} $$
Result
It is confirmed that the evaluated matrix is symmetric, as it is identical to its transposed version.
Original matrix:
Transposed matrix:
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