Matrix Multiplication - Practice Questions & MCQ

Matrix multiplication: 

Product AB can be found if the number of columns in matrix A and the number of rows in matrix B are equal. Otherwise, multiplication AB is not possible.

i) AB is defined only if col(A) = row(B)

ii) BA is defined only if col(B) = row(A)

If 

For examples

Properties of matrix multiplication:

    i) Multiplication may or may not be commutative, so AB may or may not be equal to BA.    

    ii) Matrix multiplication is associative, meaning A(BC) = (AB)C

    iii) Matrix multiplication is distributive over addition, mean  A(B+C) = AB + AC  and (B+C)A = BA + CA

    iv) If matrix multiplication of two matrices gives null matrix then it doesn’t mean that any of those two matrices was a null matrix.

             So         AB = O ⇏ A = O or B = O.

    v) Cancellation law in matrix multiplication doesn’t hold, means  AB = AC ⇏ B = C

    vi) Matrix multiplication A x A is represented by A². Thus, A・A・A・A……...n times = Aⁿ.

    vii) if A is m x n matrix then, .