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If the matrices areA =
a11 a12 a13
a21 a22 a23
a31 a32 a33
and B =
b11 b12 b13
b21 b22 b23
b31 b32 b33
then AB =
a11b11 + a12b21 + a13b31 a11b12 + a12b22 + a13b32 a11b13 + a12b23 + a13b33
a21b11 + a22b21 + a23b31 a21b12 + a22b22 + a23b32 a21b13 + a22b23 + a23b33
a31b11 + a32b21 + a33b31 a31b12 + a32b22 + a33b32 a31b13 + a32b23 + a33b33
That is true, matrix multiplication is not commutative.
Matrix addition is commutative if the elements in the matrices are themselves commutative.Matrix multiplication is not commutative.
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If an identity matrix is the answer to a problem under matrix multiplication, then each of the two matrices is an inverse matrix of the other.
It is not possible. The number of columns in the first matrix must be the same as the number of rows in the second. That is, matrices, X (kxl) and Y (mxn) can only be multiplied [in that order] if l = m.
Matrix multiplication typically refers to an operation which yields a new matrix from a pair of matrices which are already known. This is normally covered in an Algebra class or textbook.
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The time complexity of the Strassen algorithm for matrix multiplication is O(n2.81).
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A matrix is a rectangular array of elements - usually numbers. These, together with rules governing their addition and multiplication make up matrix algebra or system.