Equality of two matrix: Two matrices [a_{ij}] and [b_{ij}]
are said to be equal when they have the same number of rows and columns and a_{ij}
= b_{ij} for all admissible values of i and j.

**Definition of Equal
Matrices:**

Two matrices A and B are said to be equal if A and B have
the same order and their corresponding elements be equal. Thus if A = (a_{ij})_{m,n}
and B = (b_{ij})_{m,n} then A = B if and only if a_{ij} = b_{ij} for
i = 1, 2, 3, ....., m; j = 1, 2, 3, ......., n.

The number of rows in matrix A = The number of rows in matrix B and The number of columns in matrix A = The number of columns in matrix B

Corresponding elements of the matrix A and the matrix B are equal that is the entries of the matrix A and the matrix B in the same position are equal.

Otherwise, the matrix A and the matrix B are said to be unequal matrix and we represent A ≠ B.

Examples of Equal Matrices:

**1.** The matrices A = \(\begin{bmatrix} 5 \end{bmatrix}\) and B
= \(\begin{bmatrix} 5 \end{bmatrix}\) are equal, because both matrices are of
the same order 1 × 1 and their corresponding entries are equal.

**2.** The matrices A = \(\begin{bmatrix} 2 & 7\\ 3 & 1
\end{bmatrix}\) and B = \(\begin{bmatrix} 2 & 7\\ 3 & 1 \end{bmatrix}\)
are equal, because both matrices are of the same order 2 × 2 and their corresponding
entries are equal.

**3.** The matrices A = \(\begin{bmatrix} 4 & 6 & 1\\ 2
& 5 & 9\\ 7 & 0 & -3 \end{bmatrix}\) and B = \(\begin{bmatrix}
4 & 6 & 1\\ 2 & 5 & 9\\ 7 & 0 & -3 \end{bmatrix}\) are
equal, because both matrices are of the same order 3 × 3 and their corresponding
entries are equal.

**4.** The matrices A = \(\begin{bmatrix} 2 & -1 & 6
& 5\\ 5 & 4 & 3 & -3\\ 7 & -7 & 9 & 5\\ 2 & 3
& 8 & 4 \end{bmatrix}\) and B = \(\begin{bmatrix} 2 & -1 & 6
& 5\\ 5 & 4 & 3 & -3\\ 7 & -7 & 9 & 5\\ 2 & 3
& 8 & 4 \end{bmatrix}\) are equal, because both matrices are of the
same order 4 × 4 and their corresponding entries are equal.

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